Explanation:

- Option 1: gradually lose power or importance

- This is the correct synonym. "Wane" refers to something decreasing in power, importance, or size over time.

- Answer: This option is the most accurate.

- Option 2: useless

- "Useless" means not serving any purpose, which doesn't closely relate to "wane."

- "Wane" implies a reduction but doesn't necessarily mean completely without purpose.

- Option 3: rapid

- "Rapid" means happening in a short time or at a fast pace, the opposite of the gradual decline implied by "wane."

- Option 4: interesting

- "Interesting" indicates causing curiosity or interest, which doesn't relate to "wane."