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GUI agents are designed to automate repetitive tasks and enhance productivity. However, existing GUI agents struggle to recover once they follow an incorrect exploration path, often leading to task failure. In this work, we model GUI task execution as a DFS process and propose BEAP-Agent, a DFS-based framework that supports long-range, multi-level state backtracking with dynamic task tracking and updating. The framework consists of three collaborative components: Planner, Executor, and Tracker. Together, they enable effective task exploration and execution. BEAP-Agent fills the gap in systematic backtracking mechanisms for GUI agents, offering a systematic solution for long-horizon task exploration. We conducted a systematic evaluation on the OSWorld benchmark, where BEAP-Agent achieved an accuracy of 28.2%, validating the effectiveness of the proposed method.