...
my $previous_line;
while (my $current_line = <DATA>) {
  if ( $current_line =~ /^PLACED/
       && $previous_line =~ /^HERE IS THE DATA$/ ) {
    print $current_line;
  }
  $previous_line = $current_line;
}

##</code><code>##

...
my $seen_here_is_the_data;
while (my $line = <DATA>) {
  $seen_here_is_the_data = 1 if $line =~ /^HERE IS THE DATA$/;
  if ( $seen_here_is_the_data
       && $previous_line =~ /^HERE IS THE DATA$/ ) {
    print $line;
  }
}