
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
Given \( m \) and \( n \) as positive integers, \( A_{1}, A_{2}, \cdots, A_{m} \) are mutually non-overlapping sets each containing \( n \) positive integer elements. Furthermore, no element in \( A_{i} \) can divide any element in \( A_{i+1} \) (with index \( i \) considered modulo \( m \)), for \( i = 1, 2, \cdots, m \). Determine the maximum number of ordered pairs \( (a, b) \) where \( a \) and \( b \) are from different sets \( A_{i} \) and \( a \mid b \).

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