
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
Divide the natural numbers \(2, 3, 4, \ldots, n\) into two groups such that (1) the product of any two numbers in the same group is not in that group; (2) any number and its square are not in the same group. Find the maximum \(n\).

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