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
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:
- Start: 45 apples
- Sell 12: 45 - 12 = 33 apples
- Receive 30: 33 + 30 = 63 apples
- 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):
- [Subproblem A]
- [Subproblem B, may need A's answer]
- [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:
# [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:
- Least-to-Most: decompose into subproblems
- For each subproblem:
- PAL if computational
- ReAct if needs facts
- Tree of Thoughts if exploratory
- 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