Should I negotiate my severance? - any advice?

The company sent a severance agreement with a release of claims, and I am unsure what to do. This is my first time dealing with any of this. It includes health coverage for a couple of months. Did anyone negotiate and succeed?

An hour with an employment lawyer cost me a small fee and made me feel much safer about signing.

Read the release carefully. Mine included things I did not expect, like a non-compete.