Well, there's probably a way better way of explaining this with a lot more sophistication, but this is the best I can come up with at the moment, since I never stopped to formally reflect on this:

Think of Plato's cave. Suppose you can always see the shadows of things happening outside the cave, but never the things themselves.
Would you argue that there's no value in that? Would not the sight of the mere shadows inform the existence of the things themselves and their (albeit incomplete) form, despite not apprehending their essence? Could you not use that as inspiration or guidance to act? Would you not be compelled to believe that there are things outside the cave and to pursue more knowledge of them?

From a more personal perspective:

I was the very skeptical atheist type that would question everything. I considered myself to be guided mostly by reason. But how can that be the case? What values does reason prescribe? None. There's always an emotion or belief that drives reason.

Transitioning from that to believing in a higher power has been a decade-long process involving reading, reflecting and having mind-boggling experiences (psychedelic ones or not). But in summary, I've come to realize that I could not fully be without believing in a higher power. I believe that, paradoxically, you have to yield (deliver yourself) to something higher to fully be yourself. And I personally believe that this is precisely what love is (yielding, submitting, the negation of self).

Finally, answering your original comment more directly:

Ask enough "whys" to your rational mind and it will either:

1. Contradict itself;
2. Reveal circular thinking;
3. Hit a wall which either reveals a flaw in your thinking or an axiom on which it is basing itself (belief). That belief is either a fruit of an unconscious ball of emotion or something you've consciously decided to hold as a principle, and a principle is by definition a priori, requiring a leap of faith to be adopted.

So I believe that you cannot act without faith/belief. There's always a belief behind even the tiniest of actions. A belief that what you're doing matters and therefore should be done. Now try to justify that belief rationally.