We propose a reasoning-based approach to a dialogue management for a customer support chat bot. To build a dialogue scenario, we analyze the discourse tree (DT) of an initial query of a customer support dialogue that is frequently complex and multi-sentence. We then enforce what we call complementarity relation between DT of the initial query and that of the answers, requests and responses. The chat bot finds answers, which are not only relevant by topic but also suitable for a given step of a conversation and match the question by style, argumentation patterns, communication means, experience level and other domain-independent attributes. We evaluate a performance of proposed algorithm in car repair domain and observe a 5 to 10% improvement for single and three-step dialogues respectively, in comparison with baseline approaches to dialogue management.