With the proliferation of Large Language Models (LLMs), the detection of misinformation has become increasingly important and complex. This research proposes an innovative verifiable misinformation detection LLM agent that goes beyond traditional true/false binary judgments. The agent actively verifies claims through dynamic interaction with diverse web sources, assesses information source credibility, synthesizes evidence, and provides a complete verifiable reasoning process. Our designed agent architecture includes three core tools: precise web search tool, source credibility assessment tool and numerical claim verification tool. These tools enable the agent to execute multi-step verification strategies, maintain evidence logs, and form comprehensive assessment conclusions. We evaluate using standard misinformation datasets such as FakeNewsNet, comparing with traditional machine learning models and LLMs. Evaluation metrics include standard classification metrics, quality assessment of reasoning processes, and robustness testing against rewritten content. Experimental results show that our agent outperforms baseline methods in misinformation detection accuracy, reasoning transparency, and resistance to information rewriting, providing a new paradigm for trustworthy AI-assisted fact-checking.