
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  $n\geq 2$  be a given integer. Initially, we write  $n$  sets on the blackboard and do a sequence of moves as follows: choose two sets  $A$  and  $B$  on the blackboard such that none of them is a subset of the other, and replace  $A$  and  $B$  by  $A\cap B$  and  $A\cup B$ . This is called a  $\textit{move}$ . 
Find the maximum number of moves in a sequence for all possible initial sets. 

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