Use awk to find regex of variable length and edit following lines based on length found

I am trying to edit a fastq-file with awk.

@someheader example fastq file
TGTACTTAGAGAAGCGC
+
BDDADHHIHHHIICHIG
@nextheader
CCGTAACCTGGGCAGTG
+
DDDDDHIIIIIIIIIII

What I want to achieve is:

look for the following regex: /AGATCGGAAG[ATGC]{0,24}$/ - if possible only in lines where its actually possible to find (e.g. line 2, 6, 10, x+2%4=0 basically)
If found, remove the match
Then remove the same number of characters at the end 2 lines after the current line

So far, editing one line based on the regex was no problem for me, i used:

awk '{ gsub(/AGATCGGAAG[ATGC]{0,24}$/, ""); print RLENGTH }'

But I have no idea how i can achieve deleting the same number of characters 2 lines later. I am very unexperienced and only started learning about awk, so any help is welcome.

greetings

EDIT: heres an example containing the pattern above

@HWI-ST558:329:H3K2GBCXX:1:1101:5408:2985 1:N:0:ATCACG
CCTCCCGGTCGGTGCTGAGAGAGACTGGGCTCTCTGGAACTCCACCACCGAGATCGGAAGAG
+
HHHIIIIHDHIIIHIIGHHHIHFHHCHHIE?GHHGHF?GECFEEHFHHHCHDHHHFEEHHHH

this should be the output:

@HWI-ST558:329:H3K2GBCXX:1:1101:5408:2985 1:N:0:ATCACG
CCTCCCGGTCGGTGCTGAGAGAGACTGGGCTCTCTGGAACTCCACCACCG
+
HHHIIIIHDHIIIHIIGHHHIHFHHCHHIE?GHHGHF?GECFEEHFHHHC

the file contains 40 million of these entries, with ~250k containing the pattern

Solution

This might work but since your sample input doesn't contain any lines that'd match the regexp and you didn't provide any expected output, of course it's untested:

NR%4 == 2 { match($0,/AGATCGGAAG[ATGC]{0,24}$/) }
RSTART && (NR%4 ~ /^[02]$/) { $0 = substr($0,1,RSTART-1) }
{ print }