Severance offer, what should I ask for? - 3 months and counting

The company sent a severance agreement with a release of claims, and I am unsure what to do. Any experience at all would help. It includes health coverage for a couple of months. Did anyone negotiate and succeed?

I asked for two more weeks and a neutral reference. They agreed to the reference and added a week.

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