Random123 reproducible independent and multithreaded

I wish to generate random numbers with multithreading that are independent, both within and across threads, and are reproducible in the sense that every time I run my code I get the same results.

My intention is to use Random123 and to use a different seed for each thread. How do I choose the seeds to ensure independence across threads? My current thinking is to just use the built-in rng to generate these seeds, but is that the right thing to do?