Update README.md

README.md

@@ -60,9 +60,9 @@ llm = LLM(model=model_id, max_model_len=16384)
 
 # Example problem and solution
 problem = "Solve for x: 2x + 3 = 7"
-prefix = "Step 1: Subtract 3 from both sides: 2x = 4\nStep 2: Divide by 2: x = 2"
+prefix = "Step 1: Subtract 3 from both sides: 2x = 4\nStep 2: Divide by 2: x = 1"
 
-# Format the prompt -- this is the prompt used for the results in the paper.
+# Format the prompt
 prompt = f"""You are given a math problem and a proposed step-by-step solution:
 
 [Math Problem]
@@ -78,7 +78,7 @@ Review and critique each step in the proposed solution to determine whether each
 
 prompt = tokenizer.apply_chat_template([
     {'role': "user", "content": prompt}
-], tokenize=False, add_generation_prompt=True) # construct prompt 
+], tokenize=False, add_generation_prompt=True) + "\nLet's verify step by step:"
 
 # Set sampling parameters
 sampling_params = SamplingParams(
@@ -92,23 +92,34 @@ outputs = llm.generate(prompt, sampling_params)
 verification_cot = outputs[0].outputs[0].text
 
 print(verification_cot)
-# Alright, I've got this math problem to solve: 2x + 3 = 7. And there's a proposed solution in multiple steps that I need to review and critique.
-# ...
-# Yes, that checks out. So, the solution is correct.
+"""
+Step 1: Subtract 3 from both sides: 2x = 4
+
+Critique: Starting with the equation 2x + 3 = 7, subtracting 3 from both sides is a correct operation to isolate the term with the variable. So, 2x + 3 - 3 = 7 - 3, which simplifies
+ to 2x = 4. This step seems correct.
+
+Step 2: Divide by 2: x = 1
+
+Critique: Now, to solve for x, we need to divide both sides of the equation by 2. So, 2x / 2 = 4 / 2, which simplifies to x = 2. Wait a minute, the solution says x = 1, but accordin
+g to this calculation, it should be x = 2. This seems incorrect.
+
+Therefore, the first step is correct, but the second step has an error.
+
+**Final Output:**
 
-# Alternatively, I could think about it differently. Maybe I could first divide both sides by 2, but that would give me x + 1.5 = 3.5, and then subtract 1.5 from both sides to get x = 2. But that's more complicated than the given solution.
+Let's verify step by step:
 
-# The given solution is straightforward and efficient.
+Step 1: Subtract 3 from both sides: 2x = 4
 
-# So, in conclusion, both steps are correct, and the solution is accurate.
+Critique: This step is correct. Subtracting 3 from both sides of the equation 2x + 3 = 7 properly isolates the term with the variable, resulting in 2x = 4.
 
-# But according to the instructions, since both steps are correct, I don't need to go into more detail. I just need to state that each step is correct.
+Step 1 is \boxed{correct}
 
-# So, my output should be:
+Step 2: Divide by 2: x = 1
 
-# Step 1: The step is to subtract 3 from both sides, resulting in 2x = 4. This is a correct operation to isolate the term with x. The step is \boxed{correct}
-#
-## Step 2: The step is to divide both sides by 2, resulting in x = 2. This is the correct operation to solve for x. The step is \boxed{correct}
+Critique: This step is incorrect. Dividing both sides of the equation 2x = 4 by 2 should yield x = 2, not x = 1.
 
-# </think>
-# Is the solution correct? Yes 
+Step 2 is \boxed{incorrect}
+</think>
+Is the solution correct? No
+"""