#!/usr/bin/perl
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no strict;  # Yuk!  
no warnings;  # Yuk!
# s/no/use/gsm;
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my $step1;
my $step2;
my $step3;
my @array1;
my @array;
my $i = 0;
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• Avoid predeclaring long lists of variables,
• don't do this, use a hash, instead!

open(FILE, "assign");
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open my $fh, '<', 'assign' or
  die "hard, but say why (\$!): $!\n";
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$line = <FILE>;
while ($line ne ""){
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Huh?!? Do you mean to iterate over the lines of your file? If so... the you're not doing it. Just do it the perl idiomatic way:

while (<$fh>) { ... # or
while (my $line=<$fh>) { ...
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        chomp($line);
        if($line =~ /^(\S+)\s+(\d+)$/) {
                print "inside\n";
                $hash{$1} = $2;
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So you are using a hash after all! Then stop here and stick with it!! Don't try useless symref hacking...

                $i++;
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Am I missing something or are you doing... ehm! nothing, with that self mainteined counter?

while( ($key, $value) = each %hash) {
        print "$key +> $value\n";
        $key = $value;
}
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Worth repeating: don't! (even if you knew how to do it correctly!)

Proof of concept:

#!/usr/bin/perl -ln

use strict;
use warnings;

BEGIN { @ARGV='assign' }

our %hash;
$hash{$1}=$2 if /^(\S+)\s+(\d+)/;

END {
    my @msg=qw/FOO 1st 2nd 3rd/;
    $hash{"\$step$_"} and print $msg[$_] for 1..3;
}

__END__
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