Imagine you are a lead AI engineer at a company developing a system to solve complex, multi-stage mathematical proofs, where a single logical misstep invalidates the entire solution. The management team is debating two development strategies:

1. Strategy Alpha: Focus all computational resources on generating many complete, end-to-end proofs and then use a final verifier to check which ones are correct.
2. Strategy Beta: Allocate resources to a system that generates one step of a proof at a time, with a verifier checking the validity of each step before proceeding to the next.

Write a recommendation to the management team, arguing which strategy is superior for this specific task. Your argument must justify your choice by evaluating the trade-offs related to computational efficiency and the likelihood of finding a valid solution.