Do the Precogs Have Free Will?

Do the precogs have free will? At first I thought, this was an easy question, until I started to think about it. In a deterministic world, the ability to choose is merely an illusion. The precogs choices are influenced by prior conditions, and the freedom comes from the fact that they do not know the outcome. The precogs gifted with their vision will know their choice every time. All choices have been already made we just act them out. Both determinism and indeterminism consider that causation is incompatible with free will. They assume that if choices and decisions are caused, then they cannot be free. So in a deterministic world, the precogs do not have free will, it is just an illusion. In the physical sense they are prisoners, but in the metaphorical sense they are not. I'm saying that the precogs can't have free will, it's impossible because they have free will. In a way they have free will, and in a way they don't. Their will is made up by all their experiences and earlier life. They will always choose what they think is best at the time, if they choose not to do what is best, then it's because they think it's best to do something that is not best. They can only choose one of the options, therefore they can not really decide what to do. They can only choose what they think is best, and therefore they can only choose in one way. Because of cause and effect everything is 100% predefined. No matter what they choose, it will eventually be the right or wrong decision that will lead them to their predefined outcome. It seems that the precogs had a choice of seeing the murders that did not happen or not to see them. Like I said before, this is only an illusion of free will. The precogs could have chosen not to see the murders that did not happen, or could they. Just a side note, how could the precogs see a murder if the pre-crime unit stopped the murder before it happened. Then the murder did not happen and what the precogs saw was not what actually happened in the future. On the other hand in an indeterministic world, free will is reality but precognition is impossible. The gift of the precogs invalidates the concept of free will because it suggests a deterministic, predictable nature of the universe. In such a universe, all actions have predetermined outcomes and choice is only an illusion. We are free to choose, because we don't know our choice has already been made for us. A precog however does not have that luxury. They know the future and therefore has no free will. In conclusion I submit that a precog loses the ability to choose freely, or rather the illusion we all share. If they can see the future, they know what they will do next, and therefore they no longer choose.