<human>: Can you provide a brief overview of the text?

Related to a previous question, what are some ways I can tell if my ex is single without embarrassing myself? I ran into him recently (after a year broken up). He was with a woman and I was with a friend at the library, but he stopped to chat while the woman went ahead.

Facebook doesn't make it clear if they are dating or just friends. I don't really have the courage to be bold with him because last time I saw him I was crying at our breakup (we didn't date very long, broke up because he wasn't over his ex-fiancee and I wasn't willing to wait around). Though I haven't thought of him until he added me on social media a week ago, after seeing him in person I realized that I would totally pursue him if he were single.

How do I be cool? How do I be subtle? Do I start a Facebook chat about running into him? Do I just leave it to him and assume if he doesn't contact me there is no interest?
<bot>: Trying to find out if a not-so-serious ex is single. How do I initiate contact after seeing him and find out without embarrassing myself?