
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
If integers \( a \) and \( b \) are neither relatively prime nor does one divide the other, then \( a \) and \( b \) are called a "union" pair. Let \( A \) be an \( n \)-element subset of the set \( M = \{1, 2, \ldots, 2017\} \), such that any two numbers in \( A \) are a "union" pair. Determine the maximum value of \( n \).

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