Triangle & competition

I have a strange scenario that I need help with:

I'm TA for a small class (I only grade and participate in discussion, I don't lecture the class), with two girls in it. Let's call them Nena and Pam. I am attracted to Pam, but it was her friend Nena who asked me out. I declined saying I already have in interest in someone else. My plan was to simply wait and then ask out Pam. I ran the situation by my advisor and she told me she trusts my judgement.

Enter a complication. Today, a male student suddenly started chatting up Pam and was being quite flirtatious. At the begining of class I distributed a handout for a journal I edit and Pam expressed interest. At the end of class, I offered Pam to write a paper with me - an offer she accepted. But seeing as this young man was flirting with her, I figure I better move quick now. Any suggestions? Should I just smoothy bring it up at a project related meeting (e.g. "now an unrelated question, how are things going with [NAME]? [RESPONSE] You know why I'm asking, right?" In that case I would need to clarify that the paper project is not b/c I want to date her, but b/c I think she's smart/intellectual (the reason I want to date her to begin with).

Advice? Thank you.

 

I understand, which is why I've checked the policy and with my advisor. I did get the clerance ahead of time. I still wanted to wait until the end of the semester but given that one student suddenly has started trying to be friendly with her, I feel I need to act soon.