Simplified Travelling Salesman in Prolog

I've looked through the similar questions but can't find anything that's relevant to my problem. I'm struggling to find an algorithm or set of 'loops' that will find a path from CityA to CityB, using a database of

distance(City1,City2,Distance)

facts. What I've managed to do so far is below, but it always backtracks at write(X), and then completes with the final iteration, which is what I want it to do but only to a certain extent.

For example, I don't want it to print out any city names that are dead ends, or to use the final iteration. I want it to basically make a path from CityA to CityB, writing the name of the cities it goes to on the path.

I hope somebody can help me!

all_possible_paths(CityA, CityB) :-
    write(CityA),
    nl,
    loop_process(CityA, CityB).

loop_process(CityA, CityB) :- 
    CityA == CityB.
loop_process(CityA, CityB) :-
    CityA \== CityB,
    distance(CityA, X, _),
    write(X),
    nl,
    loop_process(X, CityB).