This was fun
You will visit every planet- true if you stay true to your pledge. But your work will never be done.
You will not visit every planet- true if you realize the futility of your work and give it up. But you will have broken your pledge.
The hypothesis leads up to a question that has to be answered. There is no right or wrong answer. It is a crossroad in the existence of an entity who is growing up. A choice.
What I really think is that this problem is a result of a misguided conception of infinity and forever. But that does not matter to the point being made.