arXiv:2510.13214v1 Announce Type: new Abstract: Recent advances in Large Language Models (LLMs) demonstrate that chain-of-thought prompting and deep reasoning substantially enhance performance on complex tasks, and multi-agent systems can further improve accuracy by enabling model debates. However, applying deep reasoning to all problems is computationally expensive. To mitigate these costs, we propose a complementary agent system integrating small and large LLMs. The small LLM first generates an initial answer, which is then verified by the large LLM. If correct, the answer is adopted directly; otherwise, the large LLM performs in-depth reasoning. Experimental results show that, for simple problems, our approach reduces the computational cost of the large LLM by more than 50% with negligible accuracy loss, while consistently maintaining robust performance on complex tasks.