
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
There are  $n$  students sitting on a round table. You collect all of  $ n $  name tags and give them back arbitrarily. Each student gets one of  $n$  name tags. Now  $n$  students repeat following operation:
The students who have their own name tags exit the table. The other students give their name tags to the student who is sitting right to him.
Find the number of ways giving name tags such that there exist a student who don't exit the table after 4 operations.

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