One (perhaps main) reason your script didn't work as intended can be found on this line:

       if ($word =~ /^\[/ && $word =~ /$\]/)
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I think you're trying to use the dollar sign in the second regex to mean "if the word ends with a close-square-bracket", but since the dollar sign there is supposed to mean "end of string", you're supposed to place it at the end of the pattern, like this:

       if ($word =~ /^\[/ && $word =~ /\]$/)
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But as others have pointed out, there is room for quite a few other improvements to the code...