Right, so the decision to or not to inject an outside query into a particular repsonse and then iterate on the result, will be something learned by the model an

Right, so the decision to or not to inject an outside query into a particular repsonse and then iterate on the result, will be something learned by the model and therefore meta-cognitive as you say. Getting the model to a good balance of when to do so is an interesting problem. However, we at least could see whether the model tried a query and display the iterative steps it took. Then at least the cases where it did use a calculator would be verifiable.