Both humans and large language models (LLMs) perform better on some reasoning tasks when they are encouraged to think step by step. However, it is unclear whether these performance gains are based on similar principles. In this work, we investigate two hypotheses: (1) that these benefits arise due to the presence of local statistical structure in the training data, where intermediate steps of reasoning may be common but any specific reasoning trajectory is rare, and (2) that sequential processing improves reasoning by mitigating interference. Using LLMs and transformers trained on a synthetic dataset, we show how analogical distance effects previously observed in humans and LLMs may be explained by the presence of local statistical structure. Testing both humans and LLMs on a novel word analogy task, we find that interference caused by semantic similarity can hurt performance and drives humans to engage in a sequential reasoning process. Our findings show that both locality structure and interference may be key principles underlying the benefits of step-by-step thinking.