Interpolate variable in a __DATA__ block

I'm trying to get a script to interpolate variable values in a
__DATA__ block if possible. This is a kind of alternative to a full-
blown template method. I'm not sure if I can even do what I want,
hence my posting here. The following code only goes so far. It
correctly prints the value of $$dataref each time GetData is called,
but not in the while loop. This is where I'm stuck.
8<---------------------
#! /usr/bin/perl
use strict;
use warnings;

my @Blocks=qw(first second third);

foreach my $block (@Blocks)
{
GetData($block);
}

sub GetData
{
my $data=shift;
my $dataref=\$data;
print "\$\$dataref is: $$dataref\n";

while (<DATA>)
{
chomp;
if ($_ eq "<$data>")
{
next;
print "$_\n";
}
if ($_ eq "</$data>")
{
last;
}
print "$_\n";
}
}


__DATA__
<first>
This is the $$dataref chunk.
</first>
<second>
This is the $$dataref chunk.
</second>
<third>
This is the $$dataref chunk.
</third>
8<------------------------

.