What would you do if your neighbor was stealing your mail?

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I have a strange suspicion that one of my neighbors might be stealing my outgoing mail. I'm not positive. Seems everytime I put a Netflix movie in the mail box to go back to the company, it disappears in transit. Oddly enough, the movies coming from Netflix never disappear. So, I'm thinking that someone is helping themselves to my out going mail. That same person is most likely on the job or busy during the early afternoon when we get our mail. So, they miss the stuff coming in. I have no proof that he's stealing our mail, so I'm not sure what I should do about it. Should I report the theft of the movies? How can find out who is taking my mail? Please advise. What would you do? What would I do if I had proof of the thief's identity? Who would I show it to? Stealing mail is a federal crime, after all, right? Really need some answers to these questions as there are other important documents and checks that come to the same mail box and I am afraid that some loser is going to steal those as well.