While large language models (LLMs) have been increasingly deployed across tasks in language understanding and interactive decision-making, their impressive performance is largely due to the comprehensive and in-depth domain knowledge embedded within them. However, the extent of this knowledge can vary across different domains. Existing methods often assume that LLMs already possess such comprehensive and in-depth knowledge of their environment, overlooking potential gaps in their understanding of actual world dynamics. To address this gap, we introduce Discover, Verify, and Evolve (DiVE), a framework that discovers world dynamics from a small number of demonstrations, verifies the correctness of these dynamics, and evolves new, advanced dynamics tailored to the current situation. Through extensive evaluations, we analyze the impact of each component on performance and compare the automatically generated dynamics from DiVE with human-annotated world dynamics. Our results demonstrate that LLMs guided by DiVE can make better decisions, achieving rewards comparable to human players in the Crafter environment.