I am going nuts trying to figure out why the following code doesn't work

!/usr/bin/perl -w
use strict;

my $dir="/var/www/html/datadir";
#

opendir (DIR, $dir) or die "cannot open $dir";
foreach my $file (readdir(DIR)) {
  &process_file ($file);
}
closedir (DIR);

sub process_file {
  my $mm="01";
  my $yyyy="2000";
  do {
    print "MM: $mm\n\n"; # for troubleshooting
    my $yyyymm=$yyyy.$mm;
    print "YYYYMM: $yyyymm\n\n"; # for troubleshooting
    my $midxnme="index_$yyyymm.txt";
    print "MIDXNME: $midxnme\n\n"; # for troubleshooting
    my $midxfle="$search_data_dir/$midxnme";
    if($midxfle = my $file) {
      print "found $midxfle\n";
    } else {
      system ("command");
    }
    $mm++;
    print "\n\nMMnext: $mm\n\n"; # for troubleshooting
  } while ($mm <= "12");
}
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On the lines where I print out for troubleshooting the MM stays at 01 on the first one and for MMnext it goes to 02 but it just stays in that particular loop. Also, even if the $midxfle file exists it always goes to the system("command").

I need the MM to increment by 1 each time until it reaches 12. What am I doing wrong?