assert(collatz_max(10) == (9, 20))

assert(collatz_max(100) == (97, 119))

assert(collatz_max(1000) == (871, 179))

assert(collatz_max(10000) == (6171, 262))

assert(collatz_max(100000) == (77031, 351))

assert(collatz_max(1000000) == (837799, 525))