The answers are B and E.

The sentence discusses the actions an aspiring pop star should take, despite the uncertain nature of achieving fame.

A. idolatrous: "Idolatrous" refers to excessive admiration or worship, usually directed towards an idol or figure. It doesn't directly relate to the persistence or determination required by an aspiring pop star.

B. dogged: "Dogged" describes someone who shows determination, persistence, or perseverance in pursuing something, often in the face of difficulties. This word fits well in the context, suggesting that an aspiring pop star should be unwavering and determined despite challenges.

C. tenuous: "Tenuous" means having little substance or strength, usually implying a weak or fragile connection. This word contrasts with the determined actions suggested in the sentence, so it doesn't align with the context.

D. notorious: "Notorious" means well-known, typically for something negative or infamous. This word doesn't fit the context of determined actions; instead, it describes a kind of reputation, not the behavior of an aspiring pop star.

E. tenacious: "Tenacious" describes someone who is persistent, determined, and unwilling to give up easily. This word aligns well with the context, suggesting that an aspiring pop star should possess a tenacious attitude despite uncertainties in achieving fame.

F. advantageous: "Advantageous" refers to something beneficial or favorable. While it's positive, it doesn't specifically describe the determined attitude or perseverance required by an aspiring pop star.

Among the options provided, "dogged" (Option B) and "tenacious" (Option E) are the best choices that accurately describe the determined and persistent behavior an aspiring pop star should have while pursuing a career in the face of potential challenges and uncertainties regarding achieving fame.