
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 \( n \) be a positive integer greater than 1. Find the number of permutations \((a_{1}, a_{2}, \cdots, a_{n})\) of \(1, 2, \cdots, n\) such that there is exactly one \( i \in \{1, 2, \cdots, n-1\} \) where \( a_{i} > a_{i+1} \).

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