Severance and unemployment, do they overlap? - what worked for you?

I was offered severance of 4 weeks after being let go as a teaching assistant and I am unsure how it affects benefits. I have been trying to stay organised about it. I also wonder about the job-search requirement. Did you file straight away?

Before signing, I asked a friend who is a lawyer to look at the agreement. It was a short conversation and worth it.

Some states only count certain kinds of severance. A local workforce centre could tell me which.