The topology of a routing tree determines how a multi-pin net branches and shares physical wire, directly affecting wirelength, congestion, capacitance, and delay. We study a central early-stage routing problem: minimizing wirelength while bounding the root-to-sink path stretch for every sink. SALT is the state-of-the-art constructive algorithm for this problem. We ask whether language-model-guided search can discover a constructive algorithm that improves on SALT. To make this search reliable, we develop an agent framework that combines parallel exploration with independent checking. Applied to SALT, the framework discovers a structural limitation: SALT repairs one sink path at a time and therefore never jointly decides where paths sharing root-side wire should split. This sink-local choice can split the paths too early and duplicate wire. This discovery leads to Flow-Aware Breakpoint Optimization (FABO), which jointly optimizes breakpoints across root-to-sink paths that share wire while preserving every sink's stretch budget. Across 1.29 million ICCAD15 nets and SALT's 20-point stretch-tolerance schedule, FABO reduces average FLUTE-normalized wirelength at every setting, with peak same reductions of 0.83% overall and 2.66% for nets with at least 30 pins. With 1.3x SALT's runtime, FABO-FAST identifies and optimizes most nets for which FABO provides a substantial wirelength reduction. Code is available at https://github.com/DevinShang/routing-FABO.

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