Unlike existing conversational recommender systems (CRSs) that focus on simple attribute-based preference extraction and item retrieval, this paper presents "Conversational Sales (CSALES)," a novel challenge that reflects the complex decision-making processes of real-world e-commerce situations. CSALES performs preference induction, recommendation, and persuasion within an integrated conversational framework. To ensure a realistic and systematic evaluation, we present CSUSER, an evaluation protocol that includes an LLM-based user simulator that models segmented user profiles based on real-world behavioral data and provides personalized interactions. Furthermore, we propose CSI, a conversational sales agent that infers contextually relevant user profiles in advance and strategically selects actions through conversation. Experimental results show that CSI significantly improves both recommendation success rates and persuasion effectiveness across a variety of user profiles.