
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
Find the number of permutations of \( n \) distinct elements \( a_{1}, a_{2}, \cdots, a_{n} \) (with \( n \geq 3 \)) such that \( a_{1} \) is not in the 1st position, \( a_{2} \) is not in the 2nd position, and \( a_{3} \) is not in the 3rd position.

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