Only one loop is needed.

#!/bin/perl

open(IN, "file1");
open(IN2, "file2");
open(OUT, "> output");

while ($str = <IN>)
{
   chomp($str);

   $data = <IN2>;
   chomp($data);

   @box = split(/\s+/, $data);
   splice(@box, 1, 0, $str);

   print OUT (join(' ', @box) . "\n");
}
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