
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 \( I = \{1, 2, 3, \cdots, n\} \). Find the maximum positive integer \( m \) such that there exists an \( m \)-element subset \( S \) of \( I \) satisfying:
(1) No element in \( S \) is a multiple of another element in \( S \).

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