Update app.py

app.py

@@ -586,8 +586,8 @@ STRICT REQUIREMENTS:
                 response_text = f"{response_text}\n\nSymPy Verification Results:\n```\n{sympy_output}\n```\n\nVerification Analysis:\n{resolution_text}"
                 
             if has_discrepancy and revised_solution:
-                    logger.debug("Performing final verification for dproblem with discrepancy")
-                    final_verification = perform_final_verification(revised_solution)
+                    logger.debug("Performing final verification for problem with discrepancy")
+                    final_verification = perform_final_verification(revised_solution,sympy_correct)
                     response_text += "\n\nFinal Expert Verification:\n" + final_verification
         
         # Create LaTeX content
@@ -686,6 +686,7 @@ def check_and_resolve_discrepancy(initial_response, sympy_output):
            to end, including all parts that were correct and the corrections for any incorrect parts. 
            Do not refer to the original solution or say things like "the rest remains the same" - write 
            out everything in full. 
+        4. Start with "SYMPY_CORRECT: True" or "SYMPY_CORRECT: False" on its own line.
 
 Original solution:
 {initial_response}
@@ -766,17 +767,24 @@ Please maintain the same LaTeX formatting as the original solution."""
                             revised_solution = parts[1].strip()
                 except Exception as e:
                     logger.error(f"Error in solution recheck: {str(e)}")
+
+            # Parse whether SymPy was correct
+                sympy_correct = None
+                if "SYMPY_CORRECT: True" in resolution_text:
+                    sympy_correct = True
+                elif "SYMPY_CORRECT: False" in resolution_text:
+                    sympy_correct = False
         
-        return resolution_text, has_discrepancy, revised_solution
+        return resolution_text, has_discrepancy, revised_solution, sympy_correct
             
     except Exception as e:
         logger.error(f"Error in discrepancy resolution: {str(e)}")
         resolution_text = f"Error in resolution: {str(e)}"
         has_discrepancy = False  # Explicitly set in error case
         revised_solution = None
-        return resolution_text, has_discrepancy, revised_solution
+        return resolution_text, has_discrepancy, revised_solution, sympy_correct
 
-def perform_final_verification(revised_solution):
+def perform_final_verification(revised_solution, sympy_correct):
     """
     Perform a final verification of the revised solution.
     """
@@ -804,6 +812,8 @@ Please follow these steps exactly:
    - Any missing steps or assumptions
    - Any necessary additional proofs or derivations
 
+4. The answer aligns with the {'SymPy' if sympy_correct else 'original'} approach proven correct
+
 Your complete solution must:
 - Be completely self-contained
 - Not refer to the original solution
@@ -813,8 +823,7 @@ Your complete solution must:
 - When referring to the dollar as a currency, never use the `$` symbol but rather write out the word dollar
 
 Remember to write out the complete solution even if you only need to add a few steps - the goal is to have a single, complete, verified solution that includes everything necessary for full mathematical rigor.
-
-At the end if you have a different solution than the Revised Solution you verified, explain exactly why."""
+"""
 
     try:
         # Make API call for final verification