
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 set  $A=\{1,2,\ldots,n\} ,$  and  $X,Y$  be two subsets (not necessarily distinct) of  $A.$  Define that  $\textup{max} X$  and  $\textup{min} Y$  represent the greatest element of  $X$  and the least element of  $Y,$  respectively. Determine the number of two-tuples  $(X,Y)$  which satisfies  $\textup{max} X>\textup{min} Y.$ 

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