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Previous research has typically concentrated on leveraging the internal knowledge of Large Language Models (LLMs) to answer known questions (i.e., internal reasoning such as generate-then-read). In contrast, for questions that fall outside their known scope, these models rely on external knowledge retrieval to provide accurate responses (i.e., external acting such as retrieve-then-read). However, few previous works consider the compositional questions, which consist of several known and unknown sub-questions, necessitating the dynamic combination of previous two methods (i.e., internal reasoning and external acting) to achieve a better trade-off between effectiveness and efficiency. To this end, we introduce a Self Divide-and-Conquer (Self-DC) framework, accompanying with the first Compositional unknown Question-Answering dataset (CuQA). This framework enables LLMs to adaptively choose between using internal knowledge and retrieving external knowledge as needed, resulting in a better trade-off between effectiveness and efficiency. Experimental results on two datasets demonstrate that Self-DC can achieve comparable or even better performance with much fewer external calls compared with several strong baselines.