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Answer: Free indirect speech
Free indirect speech is a style of third-person narration. This style uses some of the characteristics of third-person, along with the "essence" of first person direct speech. Therefore, it represents a compromise between the characters and the narrator, as it shows the character speaking through the voice of the narrator. In this case, although the characters are not directly speaking, the narrator's statements ("Nothing could be more delightful! To be fond of dancing was a certain step towards falling in love") mimic the characters' dialogue almost perfectly, with little intervention from the narrator.