The COVID-19 infodemic calls for scalable fact-checking solutions that handle long-form misinformation with accuracy and reliability. This study presents SAFE (system for accurate fact extraction and evaluation), an agent system that combines large language models with retrieval-augmented generation (RAG) to improve automated fact-checking of long-form COVID-19 misinformation. SAFE includes two agents - one for claim extraction and another for claim verification using LOTR-RAG, which leverages a 130,000-document COVID-19 research corpus. An enhanced variant, SAFE (LOTR-RAG + SRAG), incorporates Self-RAG to refine retrieval via query rewriting. We evaluated both systems on 50 fake news articles (2-17 pages) containing 246 annotated claims (M = 4.922, SD = 3.186), labeled as true (14.1%), partly true (14.4%), false (27.0%), partly false (2.2%), and misleading (21.0%) by public health professionals. SAFE systems significantly outperformed baseline LLMs in all metrics (p < 0.001). For consistency (0-1 scale), SAFE (LOTR-RAG) scored 0.629, exceeding both SAFE (+SRAG) (0.577) and the baseline (0.279). In subjective evaluations (0-4 Likert scale), SAFE (LOTR-RAG) also achieved the highest average ratings in usefulness (3.640), clearness (3.800), and authenticity (3.526). Adding SRAG slightly reduced overall performance, except for a minor gain in clearness. SAFE demonstrates robust improvements in long-form COVID-19 fact-checking by addressing LLM limitations in consistency and explainability. The core LOTR-RAG design proved more effective than its SRAG-augmented variant, offering a strong foundation for scalable misinformation mitigation.