The solution seems obvious. What am I missing here?

use strict;
use Date::Calc qw(Add_Delta_Days);

sub two_digits {
  return sprintf("%02d",shift);
}

my $date = "05.23.2003";
my ($month,$day,$year) = split /\./,$date;
($year,$month,$day) = Add_Delta_Days($year,$month,$day, 1);
my $tomorrow = join(".", two_digits($month),two_digits($day),$year);
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