
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]


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Given that \( A \) and \( B \) are subsets of \( X = \{1, 2, \cdots, n\} \). If every element in \( A \) is strictly greater than every element in \( B \), then the ordered pair of subsets \( (A, B) \) is called "good". Find the number of "good" subset pairs of \( X \).

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