Reaction feasibility prediction, as a fundamental problem in computational chemistry, has benefited from diverse tools enabled by recent advances in artificial intelligence, particularly large language models. However, the performance of individual tools varies substantially across reactions, making it difficult for any single tool to consistently perform well across all cases. This raises a critical challenge: how to effectively leverage multiple tools to obtain more accurate feasibility predictions. To address this, we propose ARMOR, an agentic framework that explicitly models tool-specific utilities, adaptively prioritizes tools, and further resolves the potential tool conflicts to produce the final prediction for each reaction. Unlike existing approaches that rely on simple aggregation or heuristic assignment over various tools, ARMOR organizes tools into a hierarchy that prioritizes top-performing tools and defers others when needed, characterizes their strengths through tool-specific patterns, and resolves conflicts via memoryaugmented reasoning. Extensive experiments on a public dataset demonstrate that ARMOR consistently outperforms strong baselines, including single-tool methods as well as various tool aggregation and tool selection approaches. Further analysis shows that the improvements are particularly significant on reactions with conflicting tool predictions, highlighting the effectiveness of ARMOR in leveraging the complementary strengths of multiple tools. The code is available via https://anonymous.4open.science/r/ARMOR-E13F.