Questions are usually the worst way to start a conversation with someone you don't know well. Conversation research shows you 6 ways to talk first/early: self-disclosures, explanations, questions, Expressions of understanding, advice, and silence.
It's too simple to think there is one thing to do for all situations. So, describe or make up one specific situation and I'll suggest some possibilities for your thinking.
Old Professor
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When I’ve done something that makes a relationship get better or makes someone like themselves more -- it makes me like myself more.