'Reason' as in 'why we do something' is countable. 'Reason' as in 'the ability to think rationally' is not countable.

Yes. Its most common meaning is countable: There must be a reason. There were several reasons why it was the best course of action. But there's also an uncountable meaning: We had reason to believe they were lying to us.

Sorry, I know this doesn't belong here but it seemed too perfect: "Le cœur a ses raisons que la raison ne connaît point"