LaTeX Delimited Answer Extraction

When evaluating large language models (LLMs) on mathematical reasoning benchmarks, a critical challenge is extracting structured final answers from free-form text responses. Models are typically prompted to enclose their definitive answer within a specific delimiter pattern—commonly a LaTeX-style command like \boxed{...}—to distinguish the final result from intermediate reasoning steps.

Implementing a robust answer extraction mechanism is essential for automated evaluation pipelines. The extractor must handle various complexities including nested delimiters (when the answer itself contains mathematical expressions with braces), multiple answer candidates (when a model revises its answer during reasoning), and edge cases where no valid answer delimiter exists.

Problem Statement:

Given a string representing a model's complete response to a mathematical problem, implement a function that extracts the content within the \boxed{} delimiter. Your implementation must:

1. Locate the \boxed{} pattern: Identify occurrences of the literal string \boxed{ followed by content and a matching closing brace
2. Handle nested braces correctly: Mathematical expressions like \frac{1}{2} or \sqrt{x^{2}+y^{2}} contain nested braces that must be parsed properly
3. Return the last occurrence: When multiple \boxed{} expressions exist (indicating answer revisions), extract from the final one
4. Return empty string on failure: If no valid \boxed{} pattern is found, return an empty string

Technical Details:

The brace-matching algorithm maintains a depth counter initialized to 1 after encountering the opening brace of \boxed{. For each subsequent character:

• Increment depth when encountering {
• Decrement depth when encountering }
• When depth reaches 0, the matching closing brace has been found

Note: The input contains literal backslash characters followed by "boxed{", not rendered LaTeX. You are processing raw text strings.