
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 \(a_{1}, a_{2}, \cdots, a_{n}\) be a permutation of \(1, 2, \cdots, n\) such that \(a_{i} \neq i\) for \(i = 1, 2, \cdots, n\). The number of such permutations is denoted by \(D_{n}\). Find \(D_{n}\).

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