To assist humans over extended periods in real homes, embodied agents must remember user routines, world states, and past interactions. Existing long-term memory benchmarks mainly evaluate language-centric retrieval and question answering, while embodied benchmarks often focus on short-horizon task execution without testing long-term memory use in dynamic environments. We introduce WorldLines, a project-driven benchmark for long-horizon embodied household assistance. It constructs temporally extended household traces with dialogues, actions, execution feedback, object and device state changes, and converts them into evidence-linked samples for Memory QA and Embodied Task Planning. We further propose ObsMem, an observer-grounded memory framework that maintains visibility-aware memories and action-native state trails for state-aware decisions. Experiments reveal persistent challenges in partial observability, overwritten world states, and translating long-term memory into embodied plans, while ObsMem offers a stronger reference architecture for this setting.

GUI automation faces critical challenges in dynamic environments. MLLMs suffer from two key issues: misinterpreting UI components and outdated knowledge. Traditional fine-tuning methods are costly for app-specific knowledge updates. We propose GUI-explorer, a training-free GUI agent that incorporates two fundamental mechanisms: (1) Autonomous Exploration of Function-aware Trajectory. To comprehensively cover all application functionalities, we design a Function-aware Task Goal Generator that automatically constructs exploration goals by analyzing GUI structural information (e.g., screenshots and activity hierarchies). This enables systematic exploration to collect diverse trajectories. (2) Unsupervised Mining of Transition-aware Knowledge. To establish precise screen-operation logic, we develop a Transition-aware Knowledge Extractor that extracts effective screen-operation logic through unsupervised analysis the state transition of structured interaction triples (observation, action, outcome). This eliminates the need for human involvement in knowledge extraction. With a task success rate of 53.7% on SPA-Bench and 47.4% on AndroidWorld, GUI-explorer shows significant improvements over SOTA agents. It requires no parameter updates for new apps. GUI-explorer is open-sourced and publicly available at https://github.com/JiuTian-VL/GUI-explorer.