通过云端与本地大模型协作，减少手机自动化任务中的界面信息泄露。

Mobile agents rely on Large Language Models (LLMs) to plan and execute tasks on smartphone user interfaces (UIs). While cloud-based LLMs achieve high task accuracy, they require uploading the full UI state at every step, exposing unnecessary and often irrelevant information. In contrast, local LLMs avoid UI uploads but suffer from limited capacity, resulting in lower task success rates. We propose $\textbf{CORE}$, a $\textbf{CO}$llaborative framework that combines the strengths of cloud and local LLMs to $\textbf{R}$educe UI $\textbf{E}$xposure, while maintaining task accuracy for mobile agents. CORE comprises three key components: (1) $\textbf{Layout-aware block partitioning}$, which groups semantically related UI elements based on the XML screen hierarchy; (2) $\textbf{Co-planning}$, where local and cloud LLMs collaboratively identify the current sub-task; and (3) $\textbf{Co-decision-making}$, where the local LLM ranks relevant UI blocks, and the cloud LLM selects specific UI elements within the top-ranked block. CORE further introduces a multi-round accumulation mechanism to mitigate local misjudgment or limited context. Experiments across diverse mobile apps and tasks show that CORE reduces UI exposure by up to 55.6% while maintaining task success rates slightly below cloud-only agents, effectively mitigating unnecessary privacy exposure to the cloud. The code is available at https://github.com/Entropy-Fighter/CORE.