Let's assume that God created man for no reason, that there was no purpose (or goal or plan) to our general being. If there was no overall purpose to our being, then the only thing we can say about our purpose of being is just to be, and that's it. Our purpose would be then just to be, to eat so that you may be, and to reproduce so that others may be. But if that was the case, then animals ("non-reasoning" animals) are perfectly capable of doing those 3 things: an animal can be, can eat to be, and reproduce so that others may be. And so a creature does not need the ability to reason to be, as animals can be with only instinct. So then, assuming the system of reasoning is logical and sound, there must be a reason as to why humans were given reason. Had the creator just wanted us to be, he wouldn't have given us the distinct ability to reason, and so there must be a reason he has given us reason. There must be an overall "use" or purpose of this reason. So doesn't this imply that there must be something else we were meant to do other than to be? Doesn't this mean there must be a real purpose to our creation, to our being?
You are starting from the assumption of a divine creator. A big assumption.
You are then stating there must be some justification for humanity having intelligence. "God was bored" does not seem like a suitable answer to you here. That means that there must be some sort of "divine plan" that human intelligence aided. "God was running an experiment" does not seem like an acceptable answer.
Your argument seems to boil down to "God created humans special, ergo there must be a specific purpose for which God created humans with these special qualities." This argument has issues with God, creation, divine purpose/values, creationism, predestination, ect.
So, your claim that there must be a real purpose to our being? nope.
Also, this isn't really a question in the sense of "I need to know something."
A simple way of phrasing this "question" could be:
"actions are only done with reasons, therefore god must have had a reason in giving humans reason."
Lots of big assumptions here; maybe your god was just on drugs when he created humans - it would certainly fit the manifest level of "reason" humans are supposedly blessed with.
Moreover, it is simplistic to claim that only humans can reason (though it is not totally clear this is what you are saying); just because some animals cannot reason doesn't make humans unique in possessing this quality. Indeed, the fact that there exist different levels of ability to reason among animals seems to suggest that humans don't have any unique "role" in this regard, even given the mammoth assumption of the existence of a benevolent, omniscient creator god.