
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 an integer \( n \geq 2 \). There are \( n \) sets written on the blackboard. The following operation is performed: select two sets \( A \) and \( B \) on the blackboard that do not contain each other, erase them, and then write \( A \cap B \) and \( A \cup B \). This is referred to as one operation. Continue performing this operation until, in any two sets, one set contains the other. Find the maximum possible number of operations for all initial states and operation methods.

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