It depends. Technically speaking, if you did not report all of your income originally, you are required to file an amended return. However, what you can choose to do is, after your return is accepted, enter the new w-2 and see if there is a difference in your return amounts, especially if you must pay anything back. Then, wait until you receive your refund. If your refund is the full amount you originally claimed, you should file the amend. If you received an adjusted amount, the IRS may have already made the adjustment as a math error (which occasionally they do).
The difference probably won't be much, but this is what you should do. If you see that adding the W-2 does not change the return at all, you can get by with not filing an amended return.
Again, you are best to wait until you receive your refund, as you do want to see how much of your refund you receive, and then take the appropriate action.
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