
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 \( n \) distinct real numbers, consider the set \( A_{n} \) of all their permutations. A permutation \((a_{1}, a_{2}, \cdots, a_{n}) \in A_{n}\) is called a "good permutation" if there exist exactly two different integers \( i, j \in \{1, 2, \cdots, n-1\} \) such that \( a_{i} > a_{i+1} \) and \( a_{j} > a_{j+1} \). Determine the number of "good permutations" in \( A_{n} \).

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