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. There are 10 people counting on me, so I am trying to be careful. The agreement mentions a release and a payment schedule. Did you file straight away?

Thanks for writing this out. I went through something close to it 10 months ago, and it settled down once I kept a simple log of every call and form.