What do you do when you like a girl and things are good between you but she's ta

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I like this girl, but she already has a boyfriend, I think. Last time I talked to her she said things were a bit rocky with him, and I don't know if she's dumped him. But if she hasn't what should I do? I don't want any silly answers like, punch him, or, drug him and dump him in the harbour or anything. Serious suggestions only. I think she kinda likes me but she doesn't know me very well, so obviously that is the first step, hang out a bit more.