
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 the set \( A = \{1, 2, \cdots, n\} \). \( X \) and \( Y \) are non-empty subsets of \( A \) (allowing \( X = Y \)). The maximum element in \( X \) and the minimum element in \( Y \) are denoted as \( \max X \) and \( \min Y \), respectively. Find the number of ordered pairs \((X, Y)\) such that \( \max X > \min Y \).

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