assert(collatz_max(10) == (19, 9))

assert(collatz_max(100) == (118, 97))

assert(collatz_max(1000) == (178, 871))

assert(collatz_max(10000) == (261, 6171))

assert(collatz_max(100000) == (350, 77031))

assert(collatz_max(1000000) == (524, 837799))