Does severance delay my unemployment claim? after 10 years as a store manager

I was offered severance of 10 weeks after being let go as a store manager and I am unsure how it affects benefits. Any experience at all would help. The agreement mentions a release and a payment schedule. Who should I ask before signing?

Thanks for writing this out. I went through something close to it 2 months ago, and it settled down once I kept a simple log of every call and form.