It is time-saving to build a reading assistant for customer service representations (CSRs) when reading user manuals, especially information-rich ones. Current solutions don't fit the online custom service scenarios well due to the lack of attention to user questions and possible responses. Hence, we propose to develop a time-saving and careful reading assistant for CSRs, named CARE. It can help the CSRs quickly find proper responses from the user manuals via explicit clue chains. Specifically, each of the clue chains is formed by inferring over the user manuals, starting from the question clue aligned with the user question and ending at a possible response. To overcome the shortage of supervised data, we adopt the self-supervised strategy for model learning. The offline experiment shows that CARE is efficient in automatically inferring accurate responses from the user manual. The online experiment further demonstrates the superiority of CARE to reduce CSRs' reading burden and keep high service quality, in particular with >35% decrease in time spent and keeping a >0.75 ICC score.