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Targeting long-form question-answering, chain-of-query (CoQ) has been studied, integrating chain-of-thought (CoT) with retrieval-augmented generation. CoQ answers the complex question step-by-step, through simpler subquestions (SQs) from which relevant knowledge is retrieved. By doing so, CoQ aims to improve the answer comprehensiveness and verifiability, at the expense of latency. Our first contribution is showing that the chaining often incurs harmful effects on both objectives, and SQs left unverified often fail to answer the given question. Second, we propose a better alternative to CoQ, union-of-query which adopts a factored approach to break the harmful chain. Finally, we propose to verify SQs before answers, by fine-tuning the SQ generator using verified SQs and introducing a selector verifying SQs in test time. Employing vicuna-13b, our approach, denoted by FaVe (short for Factored and Verified search), even outperforms ChatGPT baselines while maintaining efficiency.