Randomly select a line in every block of N lines

I'd like to randomly select a line after a given number of lines. For example here's my input: 8 blue 8 red 8 yellow 8 orange 3 pink 3 white 3 cyan 3 purple 1 magenta 1 black 1 green 1 brown and with random selection a line from every four lines, my output would be: 8 orange 3 pink 1 green The best I've come up with is: awk '!(NR%4){a=NR+4};NR<=a|"shuf -n 1"' but it doesn't work.