
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
From 49 balls numbered 1 to 49, select some balls and arrange them in a circle so that the product of the numbers on any two adjacent balls is less than 100. What is the maximum number of balls that can be selected?

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