
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 the natural numbers $1, 2, \ldots, 101$, select a group of numbers such that the greatest common divisor of any two numbers in the group is greater than two. What is the maximum number of such numbers in this group?

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