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Many iTunes songs include Digital Rights Protection which blocks them from being used in a video project.
There are ways to work around it (burn a CD of the song and then rip the song back to your computer as a WAV file), but the easiest solution is to purchase music you want to use in a project from Amazon.com, which doesn't have such stringent copy protection.
Convert your .m4a to .wav in iTunes.
I have iTunes but no .m4a to road test this. But, this should work.
It should be quick and easy.
Please let us know the results when you import your .wav into Premiere Elements 12 with its Add Media/Files and Folders/Project Assets.