Spoken dialogue systems (SDSs) have been separately developed under two different categories, task-oriented and chit-chat. The former focuses on achieving functional goals and the latter aims at creating engaging social conversations without special goals. Creating a unified conversational model that can engage in both chit-chat and task-oriented dialogue is a promising research topic in recent years. However, the potential ``initiative'' that occurs when there is a change between dialogue modes in one dialogue has rarely been explored. In this work, we investigate two kinds of dialogue scenarios, one starts from chit-chat implicitly involving task-related topics and finally switching to task-oriented requests; the other starts from task-oriented interaction and eventually changes to casual chat after all requested information is provided. We contribute two efficient prompt models which can proactively generate a transition sentence to trigger system-initiated transitions in a unified dialogue model. One is a discrete prompt model trained with two discrete tokens, the other one is a continuous prompt model using continuous prompt embeddings automatically generated by a classifier. We furthermore show that the continuous prompt model can also be used to guide the proactive transitions between particular domains in a multi-domain task-oriented setting.