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+# Chain-of-Thought Prompting
+
+## Overview
+
+Chain-of-Thought (CoT) prompting elicits step-by-step reasoning from LLMs, dramatically improving performance on complex reasoning, math, and logic tasks.
+
+## Core Techniques
+
+### Zero-Shot CoT
+Add a simple trigger phrase to elicit reasoning:
+
+```python
+def zero_shot_cot(query):
+    return f"""{query}
+
+Let's think step by step:"""
+
+# Example
+query = "If a train travels 60 mph for 2.5 hours, how far does it go?"
+prompt = zero_shot_cot(query)
+
+# Model output:
+# "Let's think step by step:
+# 1. Speed = 60 miles per hour
+# 2. Time = 2.5 hours
+# 3. Distance = Speed × Time
+# 4. Distance = 60 × 2.5 = 150 miles
+# Answer: 150 miles"
+```
+
+### Few-Shot CoT
+Provide examples with explicit reasoning chains:
+
+```python
+few_shot_examples = """
+Q: Roger has 5 tennis balls. He buys 2 more cans of tennis balls. Each can has 3 balls. How many tennis balls does he have now?
+A: Let's think step by step:
+1. Roger starts with 5 balls
+2. He buys 2 cans, each with 3 balls
+3. Balls from cans: 2 × 3 = 6 balls
+4. Total: 5 + 6 = 11 balls
+Answer: 11
+
+Q: The cafeteria had 23 apples. If they used 20 to make lunch and bought 6 more, how many do they have?
+A: Let's think step by step:
+1. Started with 23 apples
+2. Used 20 for lunch: 23 - 20 = 3 apples left
+3. Bought 6 more: 3 + 6 = 9 apples
+Answer: 9
+
+Q: {user_query}
+A: Let's think step by step:"""
+```
+
+### Self-Consistency
+Generate multiple reasoning paths and take the majority vote:
+
+```python
+import openai
+from collections import Counter
+
+def self_consistency_cot(query, n=5, temperature=0.7):
+    prompt = f"{query}\n\nLet's think step by step:"
+
+    responses = []
+    for _ in range(n):
+        response = openai.ChatCompletion.create(
+            model="gpt-5",
+            messages=[{"role": "user", "content": prompt}],
+            temperature=temperature
+        )
+        responses.append(extract_final_answer(response))
+
+    # Take majority vote
+    answer_counts = Counter(responses)
+    final_answer = answer_counts.most_common(1)[0][0]
+
+    return {
+        'answer': final_answer,
+        'confidence': answer_counts[final_answer] / n,
+        'all_responses': responses
+    }
+```
+
+## Advanced Patterns
+
+### Least-to-Most Prompting
+Break complex problems into simpler subproblems:
+
+```python
+def least_to_most_prompt(complex_query):
+    # Stage 1: Decomposition
+    decomp_prompt = f"""Break down this complex problem into simpler subproblems:
+
+Problem: {complex_query}
+
+Subproblems:"""
+
+    subproblems = get_llm_response(decomp_prompt)
+
+    # Stage 2: Sequential solving
+    solutions = []
+    context = ""
+
+    for subproblem in subproblems:
+        solve_prompt = f"""{context}
+
+Solve this subproblem:
+{subproblem}
+
+Solution:"""
+        solution = get_llm_response(solve_prompt)
+        solutions.append(solution)
+        context += f"\n\nPreviously solved: {subproblem}\nSolution: {solution}"
+
+    # Stage 3: Final integration
+    final_prompt = f"""Given these solutions to subproblems:
+{context}
+
+Provide the final answer to: {complex_query}
+
+Final Answer:"""
+
+    return get_llm_response(final_prompt)
+```
+
+### Tree-of-Thought (ToT)
+Explore multiple reasoning branches:
+
+```python
+class TreeOfThought:
+    def __init__(self, llm_client, max_depth=3, branches_per_step=3):
+        self.client = llm_client
+        self.max_depth = max_depth
+        self.branches_per_step = branches_per_step
+
+    def solve(self, problem):
+        # Generate initial thought branches
+        initial_thoughts = self.generate_thoughts(problem, depth=0)
+
+        # Evaluate each branch
+        best_path = None
+        best_score = -1
+
+        for thought in initial_thoughts:
+            path, score = self.explore_branch(problem, thought, depth=1)
+            if score > best_score:
+                best_score = score
+                best_path = path
+
+        return best_path
+
+    def generate_thoughts(self, problem, context="", depth=0):
+        prompt = f"""Problem: {problem}
+{context}
+
+Generate {self.branches_per_step} different next steps in solving this problem:
+
+1."""
+        response = self.client.complete(prompt)
+        return self.parse_thoughts(response)
+
+    def evaluate_thought(self, problem, thought_path):
+        prompt = f"""Problem: {problem}
+
+Reasoning path so far:
+{thought_path}
+
+Rate this reasoning path from 0-10 for:
+- Correctness
+- Likelihood of reaching solution
+- Logical coherence
+
+Score:"""
+        return float(self.client.complete(prompt))
+```
+
+### Verification Step
+Add explicit verification to catch errors:
+
+```python
+def cot_with_verification(query):
+    # Step 1: Generate reasoning and answer
+    reasoning_prompt = f"""{query}
+
+Let's solve this step by step:"""
+
+    reasoning_response = get_llm_response(reasoning_prompt)
+
+    # Step 2: Verify the reasoning
+    verification_prompt = f"""Original problem: {query}
+
+Proposed solution:
+{reasoning_response}
+
+Verify this solution by:
+1. Checking each step for logical errors
+2. Verifying arithmetic calculations
+3. Ensuring the final answer makes sense
+
+Is this solution correct? If not, what's wrong?
+
+Verification:"""
+
+    verification = get_llm_response(verification_prompt)
+
+    # Step 3: Revise if needed
+    if "incorrect" in verification.lower() or "error" in verification.lower():
+        revision_prompt = f"""The previous solution had errors:
+{verification}
+
+Please provide a corrected solution to: {query}
+
+Corrected solution:"""
+        return get_llm_response(revision_prompt)
+
+    return reasoning_response
+```
+
+## Domain-Specific CoT
+
+### Math Problems
+```python
+math_cot_template = """
+Problem: {problem}
+
+Solution:
+Step 1: Identify what we know
+- {list_known_values}
+
+Step 2: Identify what we need to find
+- {target_variable}
+
+Step 3: Choose relevant formulas
+- {formulas}
+
+Step 4: Substitute values
+- {substitution}
+
+Step 5: Calculate
+- {calculation}
+
+Step 6: Verify and state answer
+- {verification}
+
+Answer: {final_answer}
+"""
+```
+
+### Code Debugging
+```python
+debug_cot_template = """
+Code with error:
+{code}
+
+Error message:
+{error}
+
+Debugging process:
+Step 1: Understand the error message
+- {interpret_error}
+
+Step 2: Locate the problematic line
+- {identify_line}
+
+Step 3: Analyze why this line fails
+- {root_cause}
+
+Step 4: Determine the fix
+- {proposed_fix}
+
+Step 5: Verify the fix addresses the error
+- {verification}
+
+Fixed code:
+{corrected_code}
+"""
+```
+
+### Logical Reasoning
+```python
+logic_cot_template = """
+Premises:
+{premises}
+
+Question: {question}
+
+Reasoning:
+Step 1: List all given facts
+{facts}
+
+Step 2: Identify logical relationships
+{relationships}
+
+Step 3: Apply deductive reasoning
+{deductions}
+
+Step 4: Draw conclusion
+{conclusion}
+
+Answer: {final_answer}
+"""
+```
+
+## Performance Optimization
+
+### Caching Reasoning Patterns
+```python
+class ReasoningCache:
+    def __init__(self):
+        self.cache = {}
+
+    def get_similar_reasoning(self, problem, threshold=0.85):
+        problem_embedding = embed(problem)
+
+        for cached_problem, reasoning in self.cache.items():
+            similarity = cosine_similarity(
+                problem_embedding,
+                embed(cached_problem)
+            )
+            if similarity > threshold:
+                return reasoning
+
+        return None
+
+    def add_reasoning(self, problem, reasoning):
+        self.cache[problem] = reasoning
+```
+
+### Adaptive Reasoning Depth
+```python
+def adaptive_cot(problem, initial_depth=3):
+    depth = initial_depth
+
+    while depth <= 10:  # Max depth
+        response = generate_cot(problem, num_steps=depth)
+
+        # Check if solution seems complete
+        if is_solution_complete(response):
+            return response
+
+        depth += 2  # Increase reasoning depth
+
+    return response  # Return best attempt
+```
+
+## Evaluation Metrics
+
+```python
+def evaluate_cot_quality(reasoning_chain):
+    metrics = {
+        'coherence': measure_logical_coherence(reasoning_chain),
+        'completeness': check_all_steps_present(reasoning_chain),
+        'correctness': verify_final_answer(reasoning_chain),
+        'efficiency': count_unnecessary_steps(reasoning_chain),
+        'clarity': rate_explanation_clarity(reasoning_chain)
+    }
+    return metrics
+```
+
+## Best Practices
+
+1. **Clear Step Markers**: Use numbered steps or clear delimiters
+2. **Show All Work**: Don't skip steps, even obvious ones
+3. **Verify Calculations**: Add explicit verification steps
+4. **State Assumptions**: Make implicit assumptions explicit
+5. **Check Edge Cases**: Consider boundary conditions
+6. **Use Examples**: Show the reasoning pattern with examples first
+
+## Common Pitfalls
+
+- **Premature Conclusions**: Jumping to answer without full reasoning
+- **Circular Logic**: Using the conclusion to justify the reasoning
+- **Missing Steps**: Skipping intermediate calculations
+- **Overcomplicated**: Adding unnecessary steps that confuse
+- **Inconsistent Format**: Changing step structure mid-reasoning
+
+## When to Use CoT
+
+**Use CoT for:**
+- Math and arithmetic problems
+- Logical reasoning tasks
+- Multi-step planning
+- Code generation and debugging
+- Complex decision making
+
+**Skip CoT for:**
+- Simple factual queries
+- Direct lookups
+- Creative writing
+- Tasks requiring conciseness
+- Real-time, latency-sensitive applications
+
+## Resources
+
+- Benchmark datasets for CoT evaluation
+- Pre-built CoT prompt templates
+- Reasoning verification tools
+- Step extraction and parsing utilities