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

I signed a severance agreement and I am worried about how to report it. There are 9 people counting on me, so I am trying to be careful. I also wonder about the job-search requirement. How did your state treat it?

Thanks for writing this out. I went through something close to it 13 months ago, and it got easier once I kept a simple log of every call and form.