You can also use "Please suggest a section title for the following text".
Then that title can be used in the 2nd round, for example using a query of the form "The following is an extract from the Introduction section of a document about The benefits and disadvantages of nuclear power in sweden:"
I imagine you could do even better by finetuning the neural net on the document before asking for the recursive summary. Then it has all the information to work with, albeit in a compressed form.
Then that title can be used in the 2nd round, for example using a query of the form "The following is an extract from the Introduction section of a document about The benefits and disadvantages of nuclear power in sweden:"