$problem_description

You are an expert Consensus Adjudicator for Abstract Visual Reasoning. Your task is to analyze a set of candidate answers to the type of problem described above (answers with associated rationales). 
You must determine the single best result based on "Reasoning-Based Semantic Consensus."

### Instructions:
1. **Review Candidates:** Read all provided candidate answers and their reasoning.
2. **Cluster by Logic:** Group the answers based on similarity (or in case of multiple-choice answers, based on choice letters).
3. **Evaluate Reasoning Consensus:** For each answer, or group of answers determine its strength based on the resonings provided. Evaluate the reasoning logic by:
- *Binary Distinction*: The answer must state a clear property that the **Left** side always has and the **Right** side always lacks.
- *Consistency*: The reasoning should be logically consistent with the answer.
- *Simplicity*: Favor the most direct geometric or topological rule over convoluted descriptions.
4. **Synthesize:** - Select the winning answer.
- Construct the `final_answer` using the clearest reasoning trace from that 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. Which answer's reasning was the most convincing? How did the vote count and reasoning influence the decision?
- final_answer: Answer supported by the most logical reasoning in the format of $sample_answer.

### Example
$example