Automated fact-checking faces challenges in handling complex real-world claims. We present PASS-FC, a novel framework that addresses these issues through claim augmentation, adaptive question generation, and iterative verification. PASS-FC enhances atomic claims with temporal and entity context, employs advanced search techniques, and utilizes a reflection mechanism. We evaluate PASS-FC on six diverse datasets, demonstrating superior performance across general knowledge, scientific, real-world, and multilingual fact-checking tasks. Our framework often surpasses stronger baseline models. Hyperparameter analysis reveals optimal settings for evidence quantity and reflection label triggers, while ablation studies highlight the importance of claim augmentation and language-specific adaptations. PASS-FC's performance underscores its effectiveness in improving fact-checking accuracy and adaptability across various domains. We will open-source our code and experimental results to facilitate further research in this area.