Whoa. I'm very glad it didn't come out worse. Sounds like it was actually a pretty significant collision.

I've been in way more than my share, and I know how upsetting and disorienting they can be.

One thing I do is keep my old insurance cards in the envelope in my glove box along with the current one. That way I can just add my personal contact info and give it to the other driver. I show them the current one to show that it's valid info.
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Okey-dokey. What's plan B?