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Different people have different habits of describing their intents in conversations. Some people tend to deliberate their intents in several successive utterances, i.e., they use several consistent messages for readability instead of a long sentence to express their question. This creates a predicament faced by the application of dialogue systems, especially in real-world industry scenarios, in which the dialogue system is unsure whether it should answer the query of user immediately or wait for further supplementary input. Motivated by such an interesting predicament, we define a novel Wait-or-Answer task for dialogue systems. We shed light on a new research topic about how the dialogue system can be more intelligent to behave in this Wait-or-Answer quandary. Further, we propose a predictive approach named Predict-then-Decide (PTD) to tackle this Wait-or-Answer task. More specifically, we take advantage of a decision model to help the dialogue system decide whether to wait or answer. The decision of decision model is made with the assistance of two ancillary prediction models: a user prediction and an agent prediction. The user prediction model tries to predict what the user would supplement and uses its prediction to persuade the decision model that the user has some information to add, so the dialogue system should wait. The agent prediction model tries to predict the answer of the dialogue system and convince the decision model that it is a superior choice to answer the query of user immediately since the input of user has come to an end. We conduct our experiments on two real-life scenarios and three public datasets. Experimental results on five datasets show our proposed PTD approach significantly outperforms the existing models in solving this Wait-or-Answer problem.