1. The Logic Structure:

The sentence uses a Colon (:) Support structure. The clause following the colon provides a descriptive illustration of the noun phrase in the first clause.
- The Clue: The actor has a "ubiquitous valet" (a servant everywhere) and every "capricious whim" (sudden change of mind) is "satiated" (satisfied).
- The Inference: The actor is being treated with extreme care, pampered, and overprotected. We need a word that describes a "spoiled" or "over-attended" existence.

2. Evaluating the Choices (Grammar \& Logic Audit):
- A. precarious: (Logic Trap) Means not securely held or in position; dangerously likely to fall. While fame can be precarious, the clue about having a valet suggests the opposite of a "shaky" existence.
- B. servile: (Relationship Trap) Means having or showing an excessive willingness to serve or please others. Grammar Note: While this describes the valet, the blank modifies the actor's existence. An actor does not have a "servile existence" just because she has servants; she has a "pampered" one.
- C. cosseted: (Correct) Means cared for and protected in an overindulgent way; pampered. This perfectly matches the description of someone whose every whim is satisfied by a personal attendant.
- D. exacting: (Thematic Trap) Means making great demands on one's skill, attention, or other resources. While the actor might be exacting (demanding) toward her valet, her tenure (existence) is defined by the service she receives, not the effort she puts in.
- E. ascetic: (Opposite) Means characterized by the practice of severe self-discipline and abstention from all forms of indulgence. This is the exact opposite of the "satiated whims" mentioned in the clue.