
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
In a permutation \(\{a_{1}, a_{2}, \cdots, a_{n}\}\) of the set \(\{1, 2, \cdots, n\}\), if \(a_{i} \neq i\) (\(i=1, 2, \cdots, n\)), then this permutation is called a derangement. Find the number of derangements \(D_n\).

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