A research team is evaluating a large language model's mathematical reasoning abilities using a benchmark composed of multi-step grade school word problems. They observe that when the model is prompted to provide only the final numerical answer, its accuracy is low. However, when they modify the prompt to instruct the model to first outline the sequence of calculations and logical steps it will take before providing the final answer, the model's accuracy on the benchmark improves dramatically. Analyze the underlying reasons for this significant performance improvement. In your response, break down the relationship between the structure of the problems in the benchmark and the process the model is guided to follow.