Shell Programming and Scripting

I need to read a text file and insert a string every n lines, but also have the line counter restart when I come across a header string.

Line repeating working every 3 lines using code:

Code:

sed '0~3 s/$/\nINSERT/g' < INPUT/PATH/FILE_NAME.txt > OUTPUT/PATH/FILE_NAME.txt

I cannot seem to find how to restart counter when line=Header... I have also tried using a shell command with much less success.

ex. input:
Header Line Here
dog
cat
fish
pony
horse
Header Line Here
whale
Header Line Here
shark
lizard
dolphin


required output:
Header Line Here
dog
cat
INSERT
fish
pony
horse
INSERT
bird
Header Line Here
whale
Header Line Here
shark
lizard
INSERT
dolphin

sed does not have variables and cannot count.
With awk it's simple:

Code:

awk '(++n==3) {print "INSERT"; n=0} (/Header/) {n=0} {print}' file