Clinical Computed Tomography (CT) reconstruction often faces mixed degradations, where quantum noise, streak artifacts, and geometric distortions co-occur with various compositions and severities. Recently, all-in-one frameworks have outperformed traditional single-task models through degradation-specialized modulation mechanisms. However, attempting to resolve these mixed degradations simultaneously forces the model into suboptimal trade-offs, failing to balance conflicting reconstruction objectives. Our empirical study shows that decomposing CT reconstruction into a sequence of ordered steps effectively mitigates this conflict, with the execution order being a critical performance factor. Leveraging this insight, we propose AgenticCT, an LLM-orchestrated multi-agent framework designed to autonomously plan the optimal reconstruction trajectory. Specifically, AgenticCT operates through a diagnose-plan-treat workflow: a Supervisor Agent explicitly estimates a structured degradation state; a Planner Agent then selects a topology-optimized execution order conditioned on this state; and a library of Processor Agents sequentially executes the trajectory to achieve high-fidelity reconstruction. Extensive experiments demonstrate that AgenticCT consistently improves reconstruction fidelity across single and mixed degradations, and generalizes better to out-of-distribution datasets compared with strong specialized and all-in-one baselines. Code is available at: https://github.com/yqhuang2912/AgenticCT.