Using up my quota of guesses for the day...

This will get all valid substrings of longer valid strings.

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11137405
use warnings;

my $random = join '', map qw(A C G T)[rand 4], 1 .. 50;

for my $seq ( qw( AGCAGC AATGCAATCGCAGCAGCA AGCTACCCAGCTAGGGAGCTA
  AAA_x_AAA_x_BBB_x_AAA_x_AAA_x_BBB
  ), $random )
  {
  my %found;
  $seq =~ /([A-Z]{3,}) .* \1 (?{ $found{$1}++ }) (*FAIL)/x;
  my %counts = map { $_, scalar(() = $seq =~ /$_/g) } keys %found;
  use Data::Dump 'dd'; dd "for sequence $seq", \%counts;
  }
[download]

Outputs:

("for sequence AGCAGC", { AGC => 2 })
(
  "for sequence AATGCAATCGCAGCAGCA",
  { AAT => 2, AGC => 2, CAG => 2, GCA => 4 },
)
(
  "for sequence AGCTACCCAGCTAGGGAGCTA",
  { AGC => 3, AGCT => 3, AGCTA => 3, CTA => 3, GCT => 3, GCTA => 3 },
)
(
  "for sequence AAA_x_AAA_x_BBB_x_AAA_x_AAA_x_BBB",
  { AAA => 4, BBB => 2 },
)
(
  "for sequence ATGGACTGCCTGGAAGAATCATCCATCCTGGGGCCCGGATCTTTGTACCC",
  {
    ATC   => 4,
    ATCC  => 2,
    CAT   => 2,
    CATC  => 2,
    CCC   => 2,
    CCT   => 2,
    CCTG  => 2,
    CCTGG => 2,
    CTG   => 3,
    CTGG  => 2,
    GAA   => 2,
    GCC   => 2,
    GGA   => 3,
    TCC   => 2,
    TGG   => 3,
    TGGA  => 2,
  },
)
[download]