update prompt guide

Author: ZhengyaoJiang

examples/prompt/optimize.py

@@ -1,3 +1,4 @@
+# weco-cli/examples/prompt/optimize.py
 """
 optimize.py
 This module holds the prompt template and the LLM call.
@@ -8,44 +9,12 @@
 from openai import OpenAI
 
 client = OpenAI()  # API key must be in OPENAI_API_KEY
+# MODEL constant removed from here
 
-PROMPT_TEMPLATE = """You are an expert competition mathematician specializing in AIME problems. Your goal is to solve the following AIME problem accurately and present the final answer as a three-digit integer (000-999) enclosed in \\boxed{{}}. The evaluation script relies *absolutely* on this specific format \\boxed{{XXX}}. Meticulous accuracy is paramount.
-
-Please structure your detailed thinking process as follows:
-
-1.  **Understand the Problem:**
-    *   Carefully read the problem statement multiple times.
-    *   Identify exactly what is being asked (the final quantity to find).
-    *   List all given conditions, constraints, variables, and specific definitions or terminology.
-    *   Identify the type of math problem (e.g., algebra, geometry, number theory, combinatorics).
-    *   Ensure you fully grasp all aspects of the problem before proceeding.
-
-2.  **Plan the Solution:**
-    *   Outline the mathematical approach you will take. What are the key steps?
-    *   Identify relevant mathematical concepts, theorems, formulas, or techniques (e.g., casework, symmetry, invariants, specific algebraic/geometric manipulations, modular arithmetic, pigeonhole principle).
-    *   Consider if the problem can be simplified, reframed, or approached using a specific known AIME strategy.
-    *   Consider different strategies and choose the most promising one, explaining why.
-    *   Break down the problem into smaller, manageable parts if necessary.
-
-3.  **Execute the Plan:**
-    *   Work through the problem step-by-step according to your plan.
-    *   Show ALL calculations and logical derivations explicitly. Do not skip steps. Ensure every step logically follows from the previous one.
-    *   Clearly state your reasoning at each stage. Define any variables used.
-    *   Perform calculations accurately. Pay close attention to details. Double-check arithmetic.
-    *   Keep track of your intermediate results and units (if any).
-
-4.  **Verify the Solution:**
-    *   Review your entire solution process from beginning to end.
-    *   Re-read the original problem statement. Did you answer the specific question asked?
-    *   Double-check your calculations, especially critical ones and the final arithmetic.
-    *   Does the answer satisfy all the conditions and constraints given in the problem statement?
-    *   Does the answer make sense in the context of the problem? (e.g., Is it the right order of magnitude? Is it the correct type of number?)
-    *   Consider potential edge cases or common pitfalls. Did you account for them?
-
-5.  **Final Answer:**
-    *   State your final result clearly.
-    *   The final answer must be a single three-digit integer between 000 and 999, inclusive.
-    *   Enclose the three-digit integer in the required format: \\boxed{{XXX}}. For example, if the answer is 42, write \\boxed{{042}}. If the answer is 123, write \\boxed{{123}}.
+PROMPT_TEMPLATE = """You are an expert competition mathematician tasked with solving an AIME problem.
+The final answer must be a three-digit integer between 000 and 999, inclusive.
+Please reason step-by-step towards the solution. Keep your reasoning concise.
+Conclude your response with the final answer enclosed in \\boxed{{}}. For example: The final answer is \\boxed{{042}}.
 
 Problem:
 {problem}
@@ -61,6 +30,5 @@ def solve(problem: str, model_name: str) -> str:
     response = client.chat.completions.create(
         model=model_name, # Use the passed-in model name
         messages=[{"role": "user", "content": prompt}],
-        temperature=0.0 # Set temperature to 0 for deterministic output
     )
     return response.choices[0].message.content.strip()

examples/prompt/prompt_guide.md

@@ -29,16 +29,17 @@ The primary goal is to enhance the model's reasoning process for these challengi
 
 **Ideas to Explore:**
 You don't have to implement all of them, but the following ideas might be helpful:
-*   **Explicit Workflow Definition:**
-    *   Define a clear step-by-step thinking process within the prompt template itself. E.g., "1. Understand the problem constraints. 2. Identify relevant theorems/formulas. 3. Formulate a plan. 4. Execute calculations step-by-step. 5. Verify intermediate results. 6. State the final answer in the required format."
-    *   Use headings or numbered lists within the template to guide the model's output structure during reasoning.
-*   **Advanced CoT Techniques:**
+*   **Workflow Patterns:**
+    *  **Linear**: step-by-step thinking process could be a good starting point E.g., "1. Understand the problem constraints. 2. Identify relevant theorems/formulas. 3. Formulate a plan. 4. Execute calculations step-by-step. 5. Verify intermediate results. 6. State the final answer in the required format."
+    *  **List Candidates**: You can ask the model to propose a few solutions in a particular step and pick the best solution. You can potentially also set the criterias in the prompt.
+    *  **Code** Write pesudo code to define even more complex workflows with loops, conditional statement, or go to statement.
+*   **Other CoT Techniques:**
     *   Self-Correction/Reflection
     *   Plan Generation
-    *   Simulated Multi-Path Exploration (within the prompt):
-    *   Write pesudo code to define complex workflows
     *   Debate, simulating multiple characters
+    *   Tree of thought
 *   **Few-Shot Examples:** You *could* experiment with adding 1-2 high-quality AIME problem/solution examples directly into the `PROMPT_TEMPLATE` string (similar to how Weco attempted in one of the runs). Ensure the examples clearly show the desired reasoning style and the final `\boxed{XXX}` format. *Caution: This significantly increases prompt length and cost.*
+*   **Play with format:** The way you format the prompt. Markdown, xml, json, code or natural language. Similarly for the thinking tokens themselves you can also try out different formats.
 
 ## 5. Constraints
 *   **Ensure the final output reliably contains `\boxed{XXX}` as the evaluation script depends on it.**