Large language model (LLM) agents increasingly use tools to complete tasks in stateful environments. However, many training environments remain largely static apart from changes caused by the agent's own actions, whereas external events introduced by other users, services, or sudden contingencies in real environments can invalidate ongoing plans. To address this gap, we introduce DynaWeave, an automated synthesis framework that transforms existing static tasks into verifiable dynamic scenarios. The framework generates exogenous events relevant to each task, covering changes in task requirements, environment state, and external information. It uses directed acyclic graphs (DAGs) to represent dependencies between events and an execution engine to activate them during agent interaction. A dynamic verifier revises only the evaluation checks affected by events that actually occur and retains all other checks. Using DynaWeave, we collect 2,095 verified interaction trajectories across 36 environments and use them for supervised fine-tuning of Qwen3.5 models. Experiments on Gaia2, CostBench, and ToolMaze show that DynaWeave achieves consistent improvements in overall performance across all three evaluated model sizes, increasing the task completion rate on CostBench by 67.34 percentage points and even exceeding the performance of Gemini-3.1-Pro-Preview on ToolMaze. These results support dynamic scenario synthesis as a practical approach to training agents to adapt to changing environments. Our code is available at https://github.com/Miaow-Lab/DynaWeave.

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