The spread of disinformation poses a global threat to democratic societies, necessitating robust and scalable Automated Fact-Checking (AFC) systems. The AVeriTeC Shared Task Challenge 2024 offers a realistic benchmark for text-based fact-checking methods. This paper presents Information-Retrieving Fact-Checker (InFact), an LLM-based approach that breaks down the task of claim verification into a 6-stage process, including evidence retrieval. When using GPT-4o as the backbone, InFact achieves an AVeriTeC score of 63% on the test set, outperforming all other 20 teams competing in the challenge, and establishing a new strong baseline for future text-only AFC systems. Qualitative analysis of mislabeled instances reveals that InFact often yields a more accurate conclusion than AVeriTeC’s human-annotated ground truth.