[cause],因而 + [result]
[action],从而 + [verb phrase]
[step one],进而 + [verb phrase]
从而, 进而 and 因而 all open the second clause of a written sentence and look like "and so". They differ in what the first clause is and what the second does with it.
因而 is the neutral one: the first clause is any cause, and the second is what follows from it. It can bring in a new subject.
从而 needs an action in the first clause, usually done on purpose, and the second clause is what that action accomplishes. Both clauses share a subject, and a verb follows 从而 directly.
进而 says "and building on that, further". The second clause is a further move, not a result: you understand, and then you go on to explain; one change spreads, and then it affects something larger.
A cause that is a state, or something nobody did, can't take 从而. A plain result can't take 进而.