
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 a positive integer \( n > 1 \), select two non-empty subsets \( A \) and \( B \) from the set \( S = \{1, 2, 3, \cdots, n\} \) such that the smallest number in \( B \) is greater than the largest number in \( A \). Find the total number of different ways to make such selections.

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