Retrieval-Augmented Generation (RAG) effectively enhances Large Language Models (LLMs) by incorporating retrieved external knowledge into the generation process. Reasoning models improve LLM performance in multi-hop QA tasks, which require integrating and reasoning over multiple pieces of evidence across different documents to answer a complex question. However, they often introduce substantial computational costs, including increased token consumption and inference latency. To better understand and mitigate this trade-off, we conduct a comprehensive study of reasoning strategies for reasoning models in RAG multi-hop QA tasks. Our findings reveal that reasoning models adopt structured strategies to integrate retrieved and internal knowledge, primarily following two modes: Context-Grounded Reasoning, which relies directly on retrieved content, and Knowledge-Reconciled Reasoning, which resolves conflicts or gaps using internal knowledge. To this end, we propose a novel Lightweight Rerank Reasoning Strategy Framework for RAG (LiR$^3$AG) to enable non-reasoning models to transfer reasoning strategies by restructuring retrieved evidence into coherent reasoning chains. LiR$^3$AG significantly reduce the average 98\% output tokens overhead and 58.6\% inferencing time while improving 8B non-reasoning model's F1 performance ranging from 6.2\% to 22.5\% to surpass the performance of 32B reasoning model in RAG, offering a practical and efficient path forward for RAG systems.