An AI development company is creating a sophisticated system to solve novel, complex mathematical problems. They are considering two primary approaches:

1. Approach A: Use a general-purpose large model and, for each new problem, provide it with a detailed prompt that includes several examples of solved problems to guide its reasoning.
2. Approach B: Invest significant computational resources to conduct an additional, specialized training phase for the model using a vast dataset of mathematical problems and their step-by-step solutions.

Evaluate the long-term trade-offs between these two approaches. In your analysis, justify which approach is more likely to result in a system that is not only more efficient at solving problems but also demonstrates a more fundamental and generalizable understanding of mathematical reasoning.