Severance and unemployment, do they overlap? - any advice?

I was offered severance of 7 weeks after being let go as a bank teller and I am unsure how it affects benefits. I also wonder about the job-search requirement. How did your state treat it?

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.

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