Common sense isn't deliberate...it's a subconscious processor, we just know if something "makes sense" or is "reasonable".
It's essentially logic without words- formal logical methods such as the syllogism are a verbal emulation of the natural neural processes of common sense, perhaps like the very simple and/or/nor/etc logic gates in a computer chip. The difference is that common sense is often shallow and superficial and a reflexive indeliberate form of reasoning that we are seldom aware of thus can lead people very wrong because it does not look very far or deep in to matters or present it's arguments consciously, it is given to the bias and wind of emotion blowing the arrow of reason "off target", and creating "feelings" of being right while hitting something else entirely. These are subconscious superficial reasonings we all do without thinking about it, aka "common sense" is also "prejudice" or "prejudge", which is why it so often fails. Common examples range from Einstein being the smartest person in the world, to Elvis was the greatest music legend, to being a gold toothed rap artist really does attract women just like in the videos.
Here's an analogy: common sense we all start out with it, it's quick and reflexive its like shooting a bow without sights, without much training, or method, it is just fire for effect, and when we hit the target it gives us a sense of "understanding" more or less.
Logic and reason is like putting on sights to your bow, it is much slower, but far more accurate and takes only a little training to get pretty good, and probably remains the most accurate way to shoot, plus we can communicate it to others or where to aim to get the same results. Words allow us to far better hold concepts in our mind and manipulate them, thus logic is a slow but aware mental exercise, that can compensate for the wind of bias.
"Intuitive reason" is like "intuitive aiming" in archery, it's common sense and done without words, but with such training in logic and others, that one begins to use common sense with a sight picture while aiming, such that with great practice one can shoot both very fast and very accurately without thinking about it, and even occasionally be aware of the why "it makes sense", and communicate where to shoot to others, it is a greater degree of common sense- logic that has become subconscious, and common sense that has been strengthened and honed, both by great practice in many forms.