Guys: you meet a girl who's recently been engaged, seems really out of your reach and yet still really into you. How would you, personally, handle a situation like this?

This is purely for entertainment and semi-educational purposes. :P

I intend, though, on putting out a few more questions like this (as I’m writing a story from a man’s perspective—yikes!). It’s always interesting to hear how the opposite sex would handle different situations. Getting a glimpse of the widely varied, yet somehow categorial, male mindset.