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You could, but I wouldn't trust the result. I know there's a few tests out there that can be used before you miss your period, but they cost more money and I'm not sure they're as reliable. As far as I know, most of the OTC tests can be used reliably as soon as you miss your period. I would recommend waiting the extra four days - I know it's hard, but it's better than wasting the money on a test that isn't accurate.
There are a few brands of OTC tests that allow you to test up to 5 or 6 days before your missed period. But, you have to have enough hcg (pregnancy hormone) in your system in order for them to work (just like all pregnancy tests) and there's a good chance you won't have a high enough level to get a positive result. You're better off waiting a few more days before you test. Trust me, I took about 12 tests starting immediately after I conceived this time around because I was too impatient to wait. It was silly to waste that much money when I could have just waited a week!
Read the package of the test and it will tell you how soon before your missed period you can use that one. I would try waiting til you missed one though, just so you don't get your hopes up.