Most dialog systems posit that users have figured out clear and specific goals before starting an interaction. For example, users have determined the departure, the destination, and the travel time for booking a flight. However, in many scenarios, limited by experience and knowledge, users may know what they need, but still struggle to figure out clear and specific goals by determining all the necessary slots. In this paper, we identify this challenge and make a step forward by collecting a new human-to-human mixed-type dialog corpus. It contains 5k dialog sessions and 168k utterances for 4 dialog types and 5 domains. Within each session, an agent first provides user-goal-related knowledge to help figure out clear and specific goals, and then help achieve them. Furthermore, we propose a mixed-type dialog model with a novel Prompt-based continual learning mechanism. Specifically, the mechanism enables the model to continually strengthen its ability on any specific type by utilizing existing dialog corpora effectively.