Let

$$3$x$+1$ foroddx f$($x$)=$ x$/2$ for even x

for any natural number x$.$ If you start with an integer x and iterate f $,$ you obtain a sequence, x$,$ f $($x$),$ f $($f $($x$)),....$ Stop if you ever hit $1.$ For example, if x $=17,$ you get the sequence $17,52,26,13,40,20,10,5,16,8,4,2,1.$ Extensive computer tests have shown that every starting point between $1$ and a large positive integer gives a sequence that ends in $1.$ But the question of whether all positive starting points end up at $1$ is unsolved; it is called the $3$x $+1$ problem.

Suppose that ATM were decidable by a TM H$.$ Use H to describe a TM that is guaranteed to state the answer to the $3$x $+1$ problem.