Here is your most immediate problem: push @allow_edit, $_; should be located within the action 2 if block. And also, you shouldn't be pushing $_. Instead, you should be pushing $value.

So, the if block in question should look like this:

if( $action == 2 ) {
    push @allow_edit, $value;
}
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...and push @allow_edit, $_; should be eliminated from your code altogether.

That ought to get you going. ...not necessarily how I would do it, but at least it ought to solve your immediate issue.