A different version of Rian's escape from the Skeksis carriage can be found in chapter 3 of J.M. Lee's 2018 young adult novel "Tide of the Dark Crystal" and the dream-space meeting with Aughra happens in chapter 4. However, here the events are shown from the perspective of a Grottan Gelfling named Amri who does not appear in the TV series.
The words that Aughra chants are Deatea (fire), Deratea (air), Kidakida (water) and Arugaru (earth).