
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 4 teachers teaching mathematics in 4 different classes of the same grade. Determine the number of ways the proctoring can be arranged when each teacher is not allowed to proctor their own class.

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