提出主动记忆机制，让GUI智能体更准确判断任务状态。

Mobile GUI agents increasingly face long-horizon tasks that require reading, updating, and reusing task-relevant data across pages and applications. Existing methods treat memory largely as passive storage, where past observations are accumulated and retrieved when needed. Yet retrieving a value does not reveal its current role in the workflow. The agent must still infer from accumulated records whether the value should be used now, has already been used, or must wait for a later dependency. This implicit reconstruction becomes unreliable in long trajectories with repeated values, distractors, and outdated states, causing repeated or missed operations. To address this, we propose Active Task Driving Memory (ATMem), which shifts GUI-agent memory from passive storage to an actively maintained execution state. ATMem maintains task-relevant information as a continually updated execution state that links each value to its role and current status, enabling action selection based on the current workflow state. While supervised fine-tuning enables the agent to construct ATMem, it does not teach when ATMem is beneficial. We therefore introduce STR-GRPO, an online reinforcement learning method that encourages selective use of ATMem based on its contribution to task completion. STR-GRPO contrasts memory-on and memory-off rollouts to estimate when memory use improves execution, while memory-cost-aware reward discourages costly memory usage that does not improve execution. To evaluate whether agents can complete all in-scope work while avoiding out-of-scope actions, we build a challenging mobile benchmark. From a list of near identical entries, agents must act on every entry that satisfies the instruction and reject entries that violate its constraints. We further introduce App-Level Progress and Scope-Aware F1 to measure these two dimensions separately.