Large language models (LLMs) have shown remarkable capabilities in solving complex tasks. Recent work has explored decomposing such tasks into subtasks with independent contexts. However, some contextually related subtasks may encounter information loss during execution, leading to redundant operations or execution failures. To address this issue, we propose a training-free framework with an interaction mechanism, which enables a subtask to query specific information or trigger certain actions in completed subtasks by sending requests. To implement interaction, we introduce a subtask trajectory memory to enable resumption of completed subtasks upon receiving interaction requests. Additionally, we propose a new action during execution, which generates a concise and precise description of execution process and outcomes of a subtask, to assist subsequent subtasks in determining interaction targets and requests. We evaluate our framework on interactive decision-making task WebShop and multi-hop question answering HotpotQA, with GPT-3.5 and GPT-4, and comparison results show that our framework outperforms the state-of-the-art training-free baselines.