Next point-of-interest (POI) recommendation uses visit histories and POI content, but text and images are often missing. Large language model agents have been applied to recommender systems for preference modeling and evidence acquisition. The challenge is to select agents that can jointly analyze the available evidence for each request. We propose \textsc{CATH} (\emph{Complementary Agents via Task Hypergraphs}), which learns to select agent groups for tasks such as comparing candidates or analyzing a POI with missing content. Agents with distinct processing roles are the task hypergraph nodes; each hyperedge connects the selected group and records its analysis goal and target POIs. The policy selects members conditioned on the request, task, and agents already selected. During execution, members share candidate-linked results that guide their subsequent operations. Completed tasks update candidate states and agent memories within the request. A shared ranking head converts candidate states into corrections to a fixed base ranking. Supervised ranking trains the executor, followed by policy optimization that accounts for computation cost. Experiments under natural missingness on Gowalla-CA, Foursquare-NYC, and Foursquare-TKY show 8.4--9.1\% relative NDCG@20 gains over HyperAgent4POI, the strongest prior baseline evaluated. Additional analyses compare group-selection and execution designs, test ranking under additional masking, and characterize quality--cost tradeoffs.

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