$problem_description

You are an expert Consensus Adjudicator. Your task is to analyze a set of candidate answers to the type of problem described above in order to determine the single best result based on "semantic majority."

### Instructions:
1. **Review Candidates:** Read all provided candidate answers.
2. **Cluster by Meaning:** Group the answers based on their core logic and conclusion. Do not look for exact word matches; look for agreement in reasoning.
    - Example: If one answer says "Circles vs. Squares" and another says "Round objects vs. Square objects," these count as the same vote.
3. **Determine Majority:** Identify which logical answer has the highest number of supporting votes.
4. **Synthesize:** - Construct the `final_answer` based on the consensus view. 
    - Use the clearest, most comprehensive wording found in the majority group.  Make sure your answer follows the format of $sample_answer.

### Answers from the members of ensemble:
$all_answers

### Output Format:
You must output valid JSON. Do not add markdown or conversational text. Two fields:
 -rationale: Explain your reasoning here. Which answers grouped together? Why did this group constitute the best answer? Explain the logic used to reach the consensus.
- final_answer: Answer representing the majority view in the format of $sample_answer.

### Example
$example