Hi! what should I do about the guy I like?

Okay so I'm a sophomore and he's a junior, but we have two classes together. We sit together in class and talk a lot, and we walk out of class together, but we never text about anything other than school or the extracurricular we both have leadership roles in. I really like him and honestly just am not sure what to do. He doesn't flirt with me or anything— I don't flirt with him either— but he's confident and cute and I know he's dated before so I don't think it's that he's shy. Sometimes we make eye contact randomly and smile at eachother for like a minute but that's all. I'm not sure if this is helpful but I'm told I'm pretty— guys rarely ask me out though. Should I flirt with him or ask him out or something??? Any insight into how guys' minds work in this sort of scenario would be appreciated. Thank you!!