Final answer:
The sound of the brook getting louder is the detail that best advances the action by prompting the character to move and engage in further dialogue about the treasure.
Step-by-step explanation:
The detail from the setting that best advances the action of the scene in the excerpt from Between the Silver and the Ash is when the brook gets louder. This auditory cue indicates a change in the atmosphere, prompting Xavier to jump up and run to the back of the stage, which then leads to the action that unfolds involving the characters and their interaction with the spring. The subsequent dialogue between Xavier and Kenneth, where they discuss the joyous sounds of spring and the treasure hidden between the ash tree and the silver beech, ties back to the audible change in the brook's sound, showcasing its role in propelling the story forward.