
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The store has 89 gold coins with numbers ranging from 1 to 89, each priced at 30 yuan. Among them, only one is a "lucky coin." Feifei can ask an honest clerk if the number of the lucky coin is within a chosen subset of numbers. If the answer is "Yes," she needs to pay a consultation fee of 20 yuan. If the answer is "No," she needs to pay a consultation fee of 10 yuan. She can also choose not to ask any questions and directly buy some coins. What is the minimum amount of money (in yuan) Feifei needs to pay to guarantee she gets the lucky coin?

Present the answer in LaTex format: \boxed{Your answer}
user