Imagine you are developing a system to evaluate the quality of reasoning paths generated by an AI. You are considering two different architectures for your verifier model: one that acts as a binary classifier (outputting 'correct' or 'incorrect') and one that acts as a scoring model (outputting a numerical score). Analyze the trade-offs between these two approaches. In your analysis, discuss the implications of each choice regarding the granularity of feedback, the potential for identifying partially correct reasoning, and the overall utility for improving the AI's future performance.