
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
Let \( S = \{1, 2, 3, \ldots, 48, 49\} \). What is the maximum value of \( n \) such that it is possible to select \( n \) numbers from \( S \) and arrange them in a circle in such a way that the product of any two adjacent numbers in the circle is less than 100?

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