Accidentally Opened My Neighbors Mail That Was Deposited Into My Mailbox.

As the title says, I made a really stupid mistake. I live in a house divided into two units, and I had my neighbor's mail delivered I to my box. I've never had that happen, so I don't have a habit of checking the address before I open it. (Rest assured I will from now on.) I freaked out and started writing a note apologizing and explaining the mistake, put it in the opened envelope, and put it into his mailbox.
After doing this, I looked it up (which I should've done before hand bit I was just getting home from work and super tired) and saw that the best thing to do is label it as return to sender and put it back into your mailbox with the flag up. Welp, it's in his box now and I'm certainly not gonna grab it back.
So now I'm just super anxious about this and not sure what to do next or what could happen. Please help.
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