Please, show us a sample input. The code (after some tweaking) seems to produce something with files like the following:

> VILMFWCAxxxx
GACTACTACTACTACTACTACTACTACTACTACTACTACTACTACTACTACTACG
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Note that using while ($string =~ /.../) doesn't make much sense if you don't change the $string - it either doesn't match, or it matches forever. Maybe you wanted to add a /g at the end? Also, (^>) seems like a typo, did you want [^>] instead?