Select-then-Solve: Paradigm Routing as Inference-Time Optimization for LLM Agents

When an LLM-based agent improves on a task, is the gain from the model or from the reasoning paradigm wrapped around it? We study this question by comparing six inference-time paradigms, namely Direct, CoT, ReAct, Plan-Execute, Reflection, and ReCode, across four frontier LLMs and ten benchmarks, yielding roughly 18k runs. We find that reasoning structure helps dramatically on some tasks but hurts on others: ReAct improves over Direct by 44pp on GAIA, while CoT degrades performance by 15pp on HumanEval. No single paradigm dominates, and oracle per-task selection beats the best fixed paradigm by 17.1pp on average. Motivated by this complementarity, we propose a \emph{select-then-solve} approach: before answering each task, a lightweight embedding-based router selects the most suitable paradigm. Across four models, the router improves average accuracy from 47.6\% to 53.1\%, outperforming the best fixed paradigm at 50.3\% by 2.8pp and recovering up to 37\% of the oracle gap. In contrast, zero-shot self-routing only works for GPT-5 at 67.1\% and fails for weaker models, all trailing the learned router. Our results argue that reasoning paradigm selection should be a per-task decision made by a learned router, not a fixed architectural choice.