Next point-of-interest (POI) prediction supports personalized location services by anticipating users' next destinations. Recent methods leverage large language models (LLMs) for semantic reasoning and graphs for collective mobility modeling, improving POI prediction. However, three challenges still remain. Bridging LLMs' semantic reasoning and specific POI prediction remains challenging. User mobility also evolves over time, making it necessary to retain and update historical knowledge within limited LLM contexts. Meanwhile, global transition graphs smooth out time-specific category transition patterns. To address these challenges, we propose Semantic Hierarchical Agentic Reasoning for Next POI Prediction with Dynamic Memory (SHARP), an agentic hierarchical framework in which category-level reasoning guides specific POI prediction. A trajectory memory agent maintains a dynamic trajectory memory bank that preserves earlier mobility patterns and tracks behavioral changes with limited context growth. We construct multi-granularity time-aware category transition graphs with global and time-conditioned views to preserve temporal regularities obscured by global aggregation. A category predict agent combines these graphs with trajectory memory to predict likely next categories. SHARP learns semantic IDs (SIDs) through a residual-quantized variational autoencoder (RQ-VAE) to construct semantic POI representations, which are jointly optimized with a category-guided POI predictor end-to-end. On three real-world datasets, SHARP improves Acc@5 and Acc@10 by an average of 5.29 and 4.52 percentage points, respectively, over the strongest baseline.

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