Generating molecules that satisfy precise numeric constraints over multiple physicochemical properties is critical and challenging. Although large language models (LLMs) are expressive, they struggle with precise multi-objective control and numeric reasoning without external structure and feedback. We introduce M^4olGen, a fragment-level, retrieval-augmented, two-stage framework for molecule generation under multi-property constraints. Stage I : Prototype generation: a multi-agent reasoner performs retrieval-anchored, fragment-level edits to produce a candidate near the feasible region. Stage II : RL-based fine-grained optimization: a fragment-level optimizer trained with Group Relative Policy Optimization (GRPO) applies one- or multi-hop refinements to explicitly minimize the property errors toward our target while regulating edit complexity and deviation from the prototype. A large, automatically curated dataset with reasoning chains of fragment edits and measured property deltas underpins both stages, enabling deterministic, reproducible supervision and controllable multi-hop reasoning. Unlike prior work, our framework better reasons about molecules by leveraging fragments and supports controllable refinement toward numeric targets. Experiments on generation under two sets of property constraints (QED, LogP, Molecular Weight and HOMO, LUMO) show consistent gains in validity and precise satisfaction of multi-property targets, outperforming strong LLMs and graph-based algorithms.

Large language models (LLMs), trained on vast amounts of internet data, have developed a broad understanding of the world, enhancing the decision-making capabilities of embodied agents. This success is largely due to the comprehensive and in-depth domain knowledge within their training datasets. However, the extent of this knowledge can vary across different domains, and existing methods often assume that LLMs have a complete understanding of their environment, overlooking potential gaps in their grasp 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 with human-annotated world dynamics. Our results demonstrate that LLMs guided by can make better decisions, achieving rewards comparable to human players in the Crafter environment.