With the advancement of chatbots and the growing demand for automatic depression detection, identifying depression in patient conversations has gained more attention. However, prior methods often assess depression in a binary way or only a single score without diverse feedback and lack focus on enhancing dialogue responses. In this paper, we present a novel task of multi-aspect depression severity assessment via an inductive dialogue system (MaDSA), evaluating a patient's depression level on multiple criteria by incorporating an assessment-aided response generation. Further, we propose a foundational system for MaDSA, which induces psychological dialogue responses with an auxiliary emotion classification task within a hierarchical severity assessment structure. We synthesize the conversational dataset annotated with eight aspects of depression severity alongside emotion labels, proven robust via human evaluations. Experimental results show potential for our preliminary work on MaDSA.