Travelling - PD current as per June Bulletin

[marathon]

Gurus -

Need your help. I am in a fix. I am currently travelling and will re-enter US only in July. However, as per the latest visa bulletin, my PD will be current in June. In this context, what should I use to enter US? Would there be any issues at the port of entry?

Here's my current situation...

- H1B - Valid, expires in Nov

- Advanced Parole - Valid (never used)

Thanks for your help...