
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
Vasya thought of a natural number not greater than 100. Fedya asks Vasya questions of the type "What is the quotient of the division of the thought number by \( m \) ?", where \( m \) is a natural number, not smaller than 2, and Fedya chooses \( m \) himself. What is the minimum number of such questions Fedya needs to ask to guarantee determining the number thought by Vasya?

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