thought-based-reasoning

---
name: thought-based-reasoning
description: Use when facing complex reasoning tasks - multi-step math, logic puzzles, decisions with tradeoffs, problems where direct answers fail, or when you need to show your work. Triggers on arithmetic errors, shallow analysis, or "I'm not sure" hedging.
license: MIT
metadata:
  author: ClawFu
  version: 1.0.0
  mcp-server: "@clawfu/mcp-skills"
---

# Thought-Based Reasoning

## Overview

**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.

## When to Use

```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

## Quick Reference

| 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 |

## Techniques

### 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%

---

### 2. Self-Consistency

**When:** High-stakes decisions, need confidence measure

**Process:**
1. Run Zero-shot CoT 3-5 times (vary temperature if possible)
2. Collect all final answers
3. Take majority vote
4. 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

---

### 3. Tree of Thoughts

**When:** Puzzles, creative problems, need to explore alternatives

**Process:**
1. Generate 2-3 initial approaches
2. Evaluate each (promising/uncertain/dead-end)
3. Expand promising branches
4. Backtrack from dead-ends
5. Continue until solution found

**Template:**
```
[Problem]

## Branch 1: [Approach A]
Evaluation: [promising/uncertain/dead-end]
[If promising, continue...]

## Branch 2: [Approach B]
Evaluation: [promising/uncertain/dead-end]
[If dead-end, note why and stop]

## Expanding Branch 1:
### Branch 1.1: [Sub-approach]
...

## Solution found in Branch 1.1
```

**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

---

### 4. Least-to-Most Prompting

**When:** Complex problem with subproblems

**Process:**
1. Decompose into subproblems
2. Solve easiest first
3. Use solutions to solve harder ones
4. Combine for final answer

**Template:**
```
[Complex problem]

## Subproblems (easiest to hardest):
1. [Subproblem A]
2. [Subproblem B, may need A's answer]
3. [Subproblem C, needs A and B]

## Solutions:

### Subproblem 1:
[solve...]
Answer: [X]

### Subproblem 2 (using X):
[solve...]
Answer: [Y]

### Subproblem 3 (using X, Y):
[solve...]

## Final Answer:
[Combine solutions]
```

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

---

### 5. ReAct (Reasoning + Acting)

**When:** Need external information, reduce hallucination

**Process:**
1. Thought: reason about what's needed
2. Action: query external source
3. Observation: record result
4. 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

---

### 6. PAL (Program-Aided Language)

**When:** Math with computation, eliminate arithmetic errors

**Process:**
1. Translate problem to code
2. Execute code
3. Return result

**Template:**
```
[Math problem]

Let me write code to solve this:

```python
# [Problem restated as comments]
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

## Decision Matrix

| 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) |

## Common Mistakes

| 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 |

## Combining Techniques

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
```

---

## What Claude Does vs What You Decide

| 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 |

---

## Skill Boundaries

### This skill excels for:
- Math and logic problems with multiple steps
- Decisions with competing factors
- Puzzles requiring exploration
- Tasks where initial answers were wrong

### This skill is NOT ideal for:
- Simple factual recall → Direct answer is faster
- Creative writing → Different techniques apply
- Time-critical responses → CoT adds latency

---

## Skill Metadata

```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
```