The escalating challenge of misinformation, particularly in political discourse, requires advanced fact-checking solutions; this is even clearer in the more complex scenario of multimodal claims. We tackle this issue using a multimodal large language model in conjunction with retrieval-augmented generation (RAG), and introduce two novel reasoning techniques: Chain of RAG (CoRAG) and Tree of RAG (ToRAG). They fact-check multimodal claims by extracting both textual and image content, retrieving external information, and reasoning subsequent questions to be answered based on prior evidence. We achieve a weighted F1-score of 0.85, surpassing a baseline reasoning technique by 0.14 points. Human evaluation confirms that the vast majority of our generated fact-check explanations contain all information from gold standard data.