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

My employer is paying severance in instalments and I am not sure whether to file now. I am in Buffalo, in case local advice matters. I also wonder about the job-search requirement. Who should I ask before signing?

I filed on day one anyway and reported the severance honestly. The agency decided what to do about the timing.

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