Product search plays an essential role in eCommerce. It was treated as a special type of information retrieval problem. Most existing works make use of historical data to improve the search performance, which do not take the opportunity to ask for user's current interest directly. Some session-aware methods take the user's clicks within the session as implicit feedback, but it is still just a guess on user's preference. To address this problem, recent conversational or question-based search models interact with users directly for understanding the user's interest explicitly. However, most users do not have a clear picture on what to buy at the initial stage. Asking critical attributes that the user is looking for after they explored for a while should be a more efficient way to help them searching for the target items. In this paper, we propose a dual-learning model that hybrids the best from both implicit session feedback and proactively clarifying with users on the most critical questions. We first establish a novel utility score to measure whether a clicked item provides useful information for finding the target. Then we develop the dual Selection Net and Ranking Net for choosing the critical questions and ranking the items. It innovatively links traditional click-stream data and text-based questions together. To verify our proposal, we did extensive experiments on a public dataset, and our model largely outperformed other state-of-the-art methods.