thought-based-reasoning

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Thought-Based Reasoning

基于思维的推理

Overview

概述

Core principle: Making reasoning explicit improves accuracy 20-70% on complex tasks.

Instead of jumping to answers, decompose problems into steps. This catches errors, enables backtracking, and produces verifiable reasoning.

核心原则： 将推理过程显性化可使复杂任务的准确率提升20-70%。

不要直接给出答案，而是将问题拆解为多个步骤。这样可以发现错误、支持回溯，并生成可验证的推理过程。

When to Use

使用场景

dot

digraph decide {
  "Problem type?" [shape=diamond];
  "Direct answer worked?" [shape=diamond];
  "Need confidence?" [shape=diamond];
  "Use direct prompting" [shape=box];
  "Use Zero-shot CoT" [shape=box];
  "Use Self-Consistency" [shape=box];
  "Use technique from table" [shape=box];

  "Problem type?" -> "Direct answer worked?" [label="simple"];
  "Problem type?" -> "Use technique from table" [label="math/logic/creative"];
  "Direct answer worked?" -> "Use direct prompting" [label="yes"];
  "Direct answer worked?" -> "Need confidence?" [label="no"];
  "Need confidence?" -> "Use Self-Consistency" [label="yes, high stakes"];
  "Need confidence?" -> "Use Zero-shot CoT" [label="no, just need better"];
}

Use when:

Multi-step arithmetic or word problems
Logic requiring deduction chains
Decisions with multiple factors
Creative problems needing exploration
Any task where direct answer was wrong

Don't use when:

Simple factual recall
Single-step operations
Time-critical responses where accuracy tradeoff acceptable

dot

digraph decide {
  "Problem type?" [shape=diamond];
  "Direct answer worked?" [shape=diamond];
  "Need confidence?" [shape=diamond];
  "Use direct prompting" [shape=box];
  "Use Zero-shot CoT" [shape=box];
  "Use Self-Consistency" [shape=box];
  "Use technique from table" [shape=box];

  "Problem type?" -> "Direct answer worked?" [label="simple"];
  "Problem type?" -> "Use technique from table" [label="math/logic/creative"];
  "Direct answer worked?" -> "Use direct prompting" [label="yes"];
  "Direct answer worked?" -> "Need confidence?" [label="no"];
  "Need confidence?" -> "Use Self-Consistency" [label="yes, high stakes"];
  "Need confidence?" -> "Use Zero-shot CoT" [label="no, just need better"];
}

适用场景：

多步骤算术题或文字应用题
需要演绎链的逻辑题
涉及多因素的决策
需要探索思路的创造性问题
直接回答错误的任何任务

不适用场景：

简单事实回忆
单步骤操作
可接受准确率与时间权衡的时效性响应

Quick Reference

快速参考

Technique	Trigger	Template
Zero-shot CoT	Quick reasoning boost	"Let's think step by step..."
Self-Consistency	High-stakes decision	Run 3-5 paths, majority vote
Tree of Thoughts	Puzzle/creative block	Branch, evaluate, backtrack
Least-to-Most	Complex multi-part problem	Decompose → solve subproblems → combine
ReAct	Need external facts	Thought → Action → Observation loop
PAL	Math with computation	Generate code, execute it

技术	触发条件	模板
Zero-shot CoT	快速提升推理能力	"让我们一步步思考..."
Self-Consistency	高风险决策	运行3-5条推理路径，取多数票
Tree of Thoughts	谜题/创造性思维瓶颈	分支、评估、回溯
Least-to-Most	复杂多部分问题	拆解→解决子问题→整合
ReAct	需要外部事实	思维→行动→观察循环
PAL	涉及计算的数学题	生成代码并执行

Techniques

技术详解

1. Zero-shot Chain-of-Thought

When: Quick prototype, no examples available

Template:

[Problem statement]

Let's think step by step:

Example:

A store has 45 apples. They sell 12 in the morning and receive a shipment of 30.
Then they sell 18 more. How many apples remain?

Let's think step by step:
1. Start: 45 apples
2. Sell 12: 45 - 12 = 33 apples
3. Receive 30: 33 + 30 = 63 apples
4. Sell 18: 63 - 18 = 45 apples

Answer: 45 apples remain.

Accuracy gain: +20-60%

适用场景： 快速原型、无示例可用

模板：

[问题描述]

让我们一步步思考：

示例：

一家商店有45个苹果。上午卖出12个，然后收到30个的补货。之后又卖出18个。还剩多少个苹果？

让我们一步步思考：
1. 初始：45个苹果
2. 上午卖出后：45 - 12 = 33个苹果
3. 补货后：33 + 30 = 63个苹果
4. 下午卖出后：63 - 18 = 45个苹果

答案：还剩45个苹果。

准确率提升： +20-60%

2. Self-Consistency

When: High-stakes decisions, need confidence measure

Process:

Run Zero-shot CoT 3-5 times (vary temperature if possible)
Collect all final answers
Take majority vote
Report confidence as agreement ratio

Template:

[Problem]

I'll reason through this multiple ways to verify:

Path 1:
[reasoning...]
Answer: X

Path 2:
[reasoning...]
Answer: Y

Path 3:
[reasoning...]
Answer: X

Consensus: X (2/3 agreement = 67% confidence)

Accuracy gain: +10-20% over single CoT

适用场景： 高风险决策、需要置信度衡量

流程：

运行Zero-shot CoT 3-5次（可能的话调整温度参数）
收集所有最终答案
取多数票作为结果
以一致率作为置信度报告

模板：

[问题]

我将通过多种推理路径验证答案：

路径1:
[推理过程...]
答案: X

路径2:
[推理过程...]
答案: Y

路径3:
[推理过程...]
答案: X

共识: X（2/3一致=67%置信度）

准确率提升： 比单一CoT提升10-20%

3. Tree of Thoughts

When: Puzzles, creative problems, need to explore alternatives

Process:

Generate 2-3 initial approaches
Evaluate each (promising/uncertain/dead-end)
Expand promising branches
Backtrack from dead-ends
Continue until solution found

Template:

[Problem]

适用场景： 谜题、创造性问题、需要探索多种方案

流程：

生成2-3种初始思路
评估每种思路（有前景/不确定/死胡同）
拓展有前景的分支
从死胡同回溯
持续直到找到解决方案

模板：

[问题]

Branch 1: [Approach A]

分支1: [思路A]

Evaluation: [promising/uncertain/dead-end] [If promising, continue...]

评估: [有前景/不确定/死胡同] [如果有前景，继续...]

Branch 2: [Approach B]

分支2: [思路B]

Evaluation: [promising/uncertain/dead-end] [If dead-end, note why and stop]

评估: [有前景/不确定/死胡同] [如果是死胡同，说明原因并停止]

Expanding Branch 1:

拓展分支1:

Branch 1.1: [Sub-approach]

分支1.1: [子思路]

...

Solution found in Branch 1.1

在分支1.1中找到解决方案


**Example (Game of 24: make 24 from 4, 7, 8, 8):**

Branch 1: Try multiplication first

4 × 7 = 28... need to subtract 4, but only have 8,8
Evaluation: uncertain, continue

Branch 2: Try getting 3 × 8 = 24

Need to make 3 from 4, 7, 8
7 - 4 = 3 ✓
3 × 8 = 24 ✓
Evaluation: SOLUTION

Answer: (7 - 4) × 8 = 24 (using one 8, ignoring other) Wait - must use all numbers. Backtrack.

Branch 3: Use both 8s

8 + 8 = 16, need +8 from 4,7... 7-4=3, not 8
8 × 8 = 64, need to subtract 40 from 4,7... no
8 - 8 = 0, useless
8 / 8 = 1, then 4 × 7 × 1 = 28, not 24

Branch 4: Division approach

(8 - 4) = 4
8 / 4 = 2... not useful
4 / (8-8) = undefined

Branch 5: Fractions

8 / (1 - 7/8) = 8 / (1/8) = 64... no
Actually: 8 × (7 - 8/4) = 8 × (7-2) = 8 × 5 = 40

Hmm, trying more systematically...

Need operations on 4,7,8,8 = 24
(4 - 8/8) × 7 = 3 × 7 = 21
4 × (8 - 8/7)... messy
(8 - 4) × (8 - 2)... don't have 2

Let me try: 8 / (8 - 4/7)... no Try: (7 + 8/8) × 4 = 8 × 4 = 32... nope that's wrong Wait: (7 + 1) × 3 = 24, can I make 1 and 3? 8/8 = 1 ✓, but can't make 3 from just 4

Try factoring 24: 1×24, 2×12, 3×8, 4×6

3×8: need 3 from 4,7,8. (4+8)/7 ≈ 1.7, 7-4=3 ✓ but used 8 for the ×8
4×6: need 6 from 7,8,8. 8-8+7=7, (8+8)/7≈2.3, nope

Solution: (8 - 8/4) × 7 = (8 - 2) × 7 = 6 × 7 = 42... no

Actually: 4 × 8 - 8 + 7 - 7 = 32... wait no sevens wrong Let me be systematic: 4 × 8 = 32, 32 - 8 = 24 ✓ What about 7? 32 - 8 × 7/7 = 32 - 8 = 24 ✓

Answer: 4 × 8 - 8 × 7/7 = 32 - 8 = 24 Or simpler: 4 × 8 - 8 + 7 - 7 = 24 (trivially using 7-7=0)


**Accuracy gain:** +50-70% on hard puzzles

---


**示例（24点游戏：用4、7、8、8算出24）：**

分支1: 先尝试乘法

4 × 7 = 28... 需要减去4，但只剩8、8
评估: 不确定，继续

分支2: 尝试得到3 × 8 = 24

需要用4、7、8得到3
7 - 4 = 3 ✓
3 × 8 = 24 ✓
评估: 找到解决方案

答案: (7 - 4) × 8 = 24（使用一个8，忽略另一个）等等 - 必须使用所有数字。回溯。

分支3: 使用两个8

8 + 8 = 16，需要从4、7得到+8... 7-4=3，不是8
8 × 8 = 64，需要从4、7减去40... 不行
8 - 8 = 0，无用
8 / 8 = 1，然后4 × 7 × 1 = 28，不是24

分支4: 除法思路

(8 - 4) = 4
8 / 4 = 2... 没用
4 / (8-8) = 无意义

分支5: 分数运算

8 / (1 - 7/8) = 8 / (1/8) = 64... 不行
实际: 8 × (7 - 8/4) = 8 × (7-2) = 8 × 5 = 40

嗯，尝试更系统的方法...

对4、7、8、8进行运算得到24
(4 - 8/8) × 7 = 3 × 7 = 21
4 × (8 - 8/7)... 太复杂
(8 - 4) × (8 - 2)... 没有2

试试: 8 / (8 - 4/7)... 不行试试: (7 + 8/8) × 4 = 8 × 4 = 32... 不对等等: (7 + 1) × 3 = 24，能得到1和3吗？ 8/8 = 1 ✓，但无法只用4得到3

试试分解24: 1×24, 2×12, 3×8, 4×6

3×8: 需要用4、7、8得到3。(4+8)/7≈1.7，7-4=3 ✓ 但8已经用来乘8了
4×6: 需要用7、8、8得到6。8-8+7=7，(8+8)/7≈2.3，不行

解决方案: (8 - 8/4) × 7 = (8 - 2) × 7 = 6 × 7 = 42... 不对

实际: 4 × 8 - 8 + 7 - 7 = 32... 不对，7用错了让我系统化: 4 × 8 = 32, 32 - 8 = 24 ✓ 那7呢？32 - 8 × 7/7 = 32 - 8 = 24 ✓

答案: 4 × 8 - 8 × 7/7 = 32 - 8 = 24 或更简单: 4 × 8 - 8 + 7 - 7 = 24（利用7-7=0的小技巧）


**准确率提升：** 在高难度谜题上提升50-70%

---

4. Least-to-Most Prompting

When: Complex problem with subproblems

Process:

Decompose into subproblems
Solve easiest first
Use solutions to solve harder ones
Combine for final answer

Template:

[Complex problem]

适用场景： 包含子问题的复杂问题

流程：

将问题拆解为子问题
先解决最简单的子问题
用子问题的答案解决更难的问题
整合所有答案得到最终结果

模板：

[复杂问题]

Subproblems (easiest to hardest):

子问题（从易到难）:

[Subproblem A]
[Subproblem B, may need A's answer]
[Subproblem C, needs A and B]

[子问题A]
[子问题B，可能需要A的答案]
[子问题C，需要A和B的答案]

Solutions:

解决方案:

Subproblem 1:

子问题1:

[solve...] Answer: [X]

[解决过程...] 答案: [X]

Subproblem 2 (using X):

子问题2（使用X的结果）:

[solve...] Answer: [Y]

[解决过程...] 答案: [Y]

Subproblem 3 (using X, Y):

子问题3（使用X和Y的结果）:

[solve...]

[解决过程...]

Final Answer:

最终答案:

[Combine solutions]


**Accuracy gain:** +30-80% on compositional tasks

---

[整合所有子问题的解决方案]


**准确率提升：** 在组合任务上提升30-80%

---

5. ReAct (Reasoning + Acting)

When: Need external information, reduce hallucination

Process:

Thought: reason about what's needed
Action: query external source
Observation: record result
Repeat until solved

Template:

Question: [Question requiring external info]

Thought 1: I need to find [X] to answer this.
Action 1: Search/Lookup [X]
Observation 1: [Result]

Thought 2: Now I know X. I also need [Y].
Action 2: Search/Lookup [Y]
Observation 2: [Result]

Thought 3: With X and Y, I can now answer.
Answer: [Final answer grounded in observations]

Accuracy gain: +15-35%, major hallucination reduction

适用场景： 需要外部信息、减少幻觉

流程：

思维: 思考需要什么信息
行动: 查询外部来源
观察: 记录结果
重复直到问题解决

模板：

问题: [需要外部信息的问题]

思维1: 我需要找到[X]来回答这个问题。
行动1: 搜索/查找[X]
观察1: [结果]

思维2: 现在我知道了X，还需要[Y]。
行动2: 搜索/查找[Y]
观察2: [结果]

思维3: 有了X和Y，我可以回答问题了。
答案: [基于观察的最终答案]

准确率提升： +15-35%，大幅减少幻觉

6. PAL (Program-Aided Language)

When: Math with computation, eliminate arithmetic errors

Process:

Translate problem to code
Execute code
Return result

Template:

[Math problem]

Let me write code to solve this:

```python

适用场景： 涉及计算的数学题、消除算术错误

流程：

将问题转化为代码
执行代码
返回结果

模板：

[数学问题]

让我写代码来解决这个问题:

```python

[Problem restated as comments]

[问题重述为注释]

initial = 45 after_morning_sales = initial - 12 after_shipment = after_morning_sales + 30 after_afternoon_sales = after_shipment - 18 print(f"Remaining: {after_afternoon_sales}")


[Execute]
Output: Remaining: 45

Answer: 45

Accuracy gain: Eliminates arithmetic errors entirely

initial = 45 after_morning_sales = initial - 12 after_shipment = after_morning_sales + 30 after_afternoon_sales = after_shipment - 18 print(f"剩余: {after_afternoon_sales}")


[执行]
输出: 剩余: 45

答案: 45

准确率提升： 完全消除算术错误

Decision Matrix

决策矩阵

Situation	Best Technique
Quick reasoning, no examples	Zero-shot CoT
High-stakes, need confidence	Self-Consistency
Puzzle, creative, exploration needed	Tree of Thoughts
Multi-part with dependencies	Least-to-Most
Need facts, reduce hallucination	ReAct
Math with many calculations	PAL
Iterative improvement	Reflexion (run, critique, retry)

场景	最佳技术
快速推理、无示例	Zero-shot CoT
高风险、需要置信度	Self-Consistency
谜题、创造性、需要探索	Tree of Thoughts
多部分且有依赖关系	Least-to-Most
需要事实、减少幻觉	ReAct
包含大量计算的数学题	PAL
迭代改进	Reflexion（运行、评估、重试）

Common Mistakes

常见错误

Mistake	Fix
Using CoT for simple queries	Direct answer is fine for 1-step problems
Not showing work	Explicit steps catch errors
Stopping at first answer	Self-consistency finds better answers
Linear thinking on puzzles	Tree of Thoughts enables backtracking
Computing mentally	PAL eliminates arithmetic errors
Guessing facts	ReAct grounds in external sources

错误	修复方案
对简单查询使用CoT	单步骤问题直接回答即可
不展示推理过程	显性步骤可发现错误
得到第一个答案就停止	自一致性可找到更优答案
对谜题使用线性思维	Tree of Thoughts支持回溯
心算	PAL可消除算术错误
猜测事实	ReAct基于外部来源确保准确性

Combining Techniques

技术组合

For maximum accuracy on hard problems:

1. Least-to-Most: decompose into subproblems
2. For each subproblem:
   - PAL if computational
   - ReAct if needs facts
   - Tree of Thoughts if exploratory
3. Self-Consistency on final assembly

针对高难度问题实现最高准确率：

1. Least-to-Most: 将问题拆解为子问题
2. 对每个子问题:
   - 涉及计算时使用PAL
   - 需要事实时使用ReAct
   - 需要探索时使用Tree of Thoughts
3. 对最终整合结果使用Self-Consistency

What Claude Does vs What You Decide

Claude的职责与你的决策

Claude handles	You provide
Selecting appropriate reasoning technique	Problem statement and constraints
Executing multi-step reasoning chains	Verification of intermediate steps
Generating multiple reasoning paths	Selection of best answer
Backtracking from dead-ends	Judgment on acceptable confidence
Computing via PAL when needed	Real-world validation of results

Claude负责	你提供
选择合适的推理技术	问题描述与约束
执行多步骤推理链	验证中间步骤
生成多条推理路径	选择最优答案
从死胡同回溯	判断可接受的置信度
必要时通过PAL计算	结果的现实验证

Skill Boundaries

技能边界

This skill excels for:

本技能擅长：

Math and logic problems with multiple steps
Decisions with competing factors
Puzzles requiring exploration
Tasks where initial answers were wrong

多步骤数学与逻辑问题
存在竞争因素的决策
需要探索的谜题
初始答案错误的任务

This skill is NOT ideal for:

本技能不适合：

Simple factual recall → Direct answer is faster
Creative writing → Different techniques apply
Time-critical responses → CoT adds latency

简单事实回忆 → 直接回答更快
创意写作 → 需要不同技术
时效性响应 → CoT会增加延迟

Skill Metadata

技能元数据

yaml

name: thought-based-reasoning
category: thinking
version: 2.0
author: GUIA
source_expert: Wei et al. (CoT), Yao et al. (ToT), Kojima et al. (Zero-shot CoT)
difficulty: intermediate
mode: both
tags: [reasoning, cot, tot, react, pal, logic, math, problem-solving]
created: 2026-02-03
updated: 2026-02-03

yaml

name: thought-based-reasoning
category: thinking
version: 2.0
author: GUIA
source_expert: Wei et al. (CoT), Yao et al. (ToT), Kojima et al. (Zero-shot CoT)
difficulty: intermediate
mode: both
tags: [reasoning, cot, tot, react, pal, logic, math, problem-solving]
created: 2026-02-03
updated: 2026-02-03