We study the problem of providing recommended responses to customer service agents in live-chat dialogue systems. Smart-reply systems have been widely applied in real-world applications (e.g. Gmail, LinkedIn Messaging), where most of them can successfully recommend reactive responses. However, we observe a major limitation of current methods is that they generally have difficulties in suggesting proactive investigation act (e.g. "Do you perhaps have another account with us?") due to the lack of long-term context information, which indeed act as critical steps for customer service agents to collect information and resolve customers' issues. Thus in this work, we propose an end-to-end method with special focus on suggesting proactive investigative questions to customer agents in Airbnb's customer service live-chat system. Effectiveness of our proposed method can be validated through qualitative and quantitative results.