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Hierarchical dual-system methods address this but suffer from a gap between high-level planning semantics and low-level execution kinematics. We introduce Cortex, a bidirectionally aligned embodied agent framework with a customized planning interface that conveys executable and tractable subtask plans from high-level VLM to low-level VLA. Specifically, we standardize manipulation subtasks into 32 canonical skill primitives and inject tractability principles, such as representative object attributes and improved trajectory reachability, into the data generation pipeline. This enables automatic annotation of over 4k hours of open-source video data and generation of 30 hours of simulation data. 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