Does severance delay my unemployment claim? (Albuquerque)

My employer is paying severance in instalments and I am not sure whether to file now. I worked as a call-centre agent before this. 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 5 months ago, and it settled down once I kept a simple log of every call and form.