Can you get Unemployment and SS benefits at the same time?

I'm planning to retire at the end of May. If I let my employer know now, to give them time to restructure or find a new employee, they just might choose to let me go early. I could then apply for unemployment benefits, presumably. Should I then put off applying for retirement benefits from SS until after unemployment has run out? But if I do, wouldn't I be required to "look for work" to qualify for unemployment benefits, even though I'm still planning to retire in a couple of months? Presumably I can't apply for unemployment while also receiving SS retirement benefits?

I should mention that I'm in California, since the rules may be different here than elsewhere. It's been about 20 years since I've had to deal with the EDD, but I recall them pretty adamant about the "looking for work" clause to qualify for benefits. If I'm taking retirement benefits I'm presumably not looking for work. Even if I don't take my retirement benefits, I'm really not going to be wasting time looking for a job I'm not going to accept or keep.