In this work we propose a novel module for a dialogue system that allows a conversational agent to utter phrases that do not just meet the system's task intentions, but also work towards achieving the system's social intentions. The module - a Social Reasoner - takes the task goals the system must achieve and decides the appropriate conversational style and strategy with which the dialogue system describes the information the user desires so as to boost the strength of the relationship between the user and system (rapport), and therefore the user's engagement and willingness to divulge the information the agent needs to efficiently and effectively achieve the user's goals. Our Social Reasoner is inspired both by analysis of empirical data of friends and stranger dyads engaged in a task, and by prior literature in fields as diverse as reasoning processes in cognitive and social psychology, decision-making, sociolinguistics and conversational analysis. Our experiments demonstrated that, when using the Social Reasoner in a Dialogue System, the rapport level between the user and system increases in more than 35% in comparison with those cases where no Social Reasoner is used.