Should I negotiate my severance? after 15 years as a marketing coordinator

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?

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

Ask for the offer in writing and do not sign on the spot. A day or two to think is normal.