Product review summarization aims to generate a concise summary based on product reviews to facilitate purchasing decisions. This intricate task gives rise to three challenges in existing work: factual accuracy, aspect comprehensiveness, and content relevance. In this paper, we first propose an FB-Thinker framework to improve the summarization ability of LLMs with multi-objective forward reasoning and multi-reward backward refinement. To enable LLM with these dual capabilities, we present two Chinese product review summarization datasets, Product-CSum and Product-CSum-Cross, for both instruction-tuning and cross-domain evaluation. Specifically, these datasets are collected via GPT-assisted manual annotations from an online forum and public datasets. We further design an evaluation mechanism Product-Eval, integrating both automatic and human evaluation across multiple dimensions for product summarization. Experimental results show the competitiveness and generalizability of our proposed framework in the product review summarization tasks.