Are you sure that they have the right to revise your assessment upward?
If you appeal, in the hopes of a lower assessment, you are opening the door to a more "in depth" assessment. They will visit your house and they will take very careful note of what was in your original assessment vs. what the detailed inspection revealed. (Say the original assessment did not note a finished basement, and you have a finished basement, and as a result of your appeal, they carry out a detailed inspection of your home and say, "hey, this guy has a finished basement and our original assessment indicated an unfinished basement. In fact, he also has a fireplace, and central air conditioning too and his assessment didn't show that. ADD all of those to his assessment")
In other words, if you aren't 100 percent confident that your assessment is too high, don't appeal because the appeal will open the door to an in depth assessment. Your assessment you received in the mail is not the maximum. It's what they are saying your house is worth on the open market. If you reject it, all bets are off.
Yes, I've been there, I've seen first hand how it works.