In your code,

@data=<FILE>;  <-- Puts the whole file in @data
while(<FILE>)  <-- There's nothing left to read here.
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You simply want

#!/usr/bin/perl

use strict;
use warnings;

my @list;

open(my $fh, '<', $file)
   or die("Unable to open file \"$file\": $!\n");

while (<$fh>) {
   push @list, [split/s+/];
}
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