Large Language Models (LLMs) typically exhibit a performance profile where reliability degrades as task complexity increases. We address the challenge of generating high-quality natural language executable plans for complex tasks by introducing GRASP, a strategy-aware, multi-stage planning framework. GRASP decouples the planning pipeline across specialized, context-isolated modules: it pre-compiles global macro-guidelines (GenPlan), explores alternative localized strategies within isolated context windows (RevPlan), and independently evaluates trajectories using a multi-criteria discriminator (VerPlan). Empirical evaluations show that GRASP consistently establishes a new state-of-the-art frontier across diverse datasets, yielding substantial accuracy gains over direct LLM planners on Natural Plan Calendar Scheduling (?12.4%?), ZebraLogic (?30.8%?), and SciBench Math. Crucially, under multi-task scaling-where standard planners suffer immediate performance collapse-GRASP completely flattens the multi-task degradation penalty. In interleaved dual-task environments, GRASP achieves an absolute accuracy gain of up to 16.7% over direct LLM planners. Furthermore, by isolating context and enforcing strict macro-regularization, GRASP outperforms frontier reasoning models (such as GPT-5-mini) by a margin of 14.5%.