Severance and unemployment, do they overlap? after 17 years as an accountant

I was offered severance of 17 weeks after being let go as an accountant and I am unsure how it affects benefits. This is my first time dealing with any of this. The agreement mentions a release and a payment schedule. 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.