I guess if getting new data is not allowed, then interpolation or extrapolation would be the next best option. Interpolation would be connecting existing thoughts to form or find new ones in between. Extrapolation would be following a train of thought to its ultimate end. This could be done in either the diffused or focused mental states. I like to draw up diagrams for this so I can see the blank spots to fill or direction things seem to be going.

There is also the semantics of the question. It's actually quite an ancient topic, where our thoughts come from. What does "original" mean? The thought originating in our mind, or from some higher realm? I won't go too deep into this, just bringing it up to think about it. The only thing I wanted to say is that maybe our mind is not entirely free and agentive, but actually there is a "darkness that comes before" to reference The Second Apocalypse which we can't conquer, but are conquered by.

On a lighter note, and from my own experience, it is definitely possible to generate new thoughts outside of that diffuse cloud of repeated thoughts formed on the storehouse of experience accumulated so far in our lives. Following practices of mindfulness, we can learn to recognize the noise of our mind and separate those "thoughts" from what we might call more agentive thoughts that we can control over, wherever they come from. I do meditations in these styles and achieve a mental state beyond the diffuse and focused, kind of inverse to dreaming (cf. turiya for this kind of formulation of a fourth state of mind). In this state, you can come to understand things which you could probably never do in the other mental states. Those thoughts feel "cleaner" as if coming from a true origin rather than bounced around a cloud of repeated thoughts like you mention.

But I feel like maybe these thoughts are not exactly the ones you are looking for. They are removed from our everyday sense of living, and not really invested in disciplines we have come up with socially as humans. It would be like asking if a caveman 500,000 years ago would have come up with the solution to how to fix a bug in the code I just wrote. It would have been an original thought for him sure, but kind of besides the point.

Edit: as an example for the interpolation/extrapolation, consider sentences like "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo" or actual usages of this sort of thing in literature:

https://en.wikipedia.org/wiki/Kir%C4%81t%C4%81rjun%C4%ABya#Linguistic_ingenuity

https://en.wikipedia.org/wiki/Lion-Eating_Poet_in_the_Stone_Den

The interesting part is that constrained thinking is what produces this