It's not randomness it's "your thoughts on paper". That's not random, that starting with you.
I am not sure why you think logic is so central here. Of course you need logic, but it will only work if your premise is correct and IMHO if you are trying to solve a problem then most of the time it's your premise that's wrong not the logical reasoning that springs from it.
This is kind of interesting. Where does your thoughts come from? If I asked you to think of a famous person, and say the first person that comes to your mind, what determines whom you will think of? Presumably you were not thinking of a person before I asked. Did you have any choice in what person you started thinking about?
I am not sure why you think logic is so central here. Of course you need logic, but it will only work if your premise is correct and IMHO if you are trying to solve a problem then most of the time it's your premise that's wrong not the logical reasoning that springs from it.