Science

if we add true randomness to an input-based decision, it stops being predetermined, but there's still a logically conclusive choice you're going to make, based on the incomplete inputs you have. You cannot 'freely' decide to not pick that choice

I think you are contradicting yourself. If you cannot freely choose something else, then your choice is predetermined.

Whereas if a choice stops being predetermined, then there is no "logically conclusive choice" that you are definitely going to make. There is a range of possible choices, one of them is chosen by you, and the others could have been chosen but weren't.

For example, you choose a tuna salad sandwich for lunch, but you could have chosen a ham sandwich. That choice was quite possibly not determined by logic, considerations of evolutionary fitness, or genetics. If it were, then you would probably always choose tuna salad over a ham sandwich.