
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 and 4 students standing in a row for a photo. (You must write out the analytical formula before calculating the result to receive points)  
(1) If the 4 students must stand together, how many different arrangements are there?  
(2) If any two students cannot stand next to each other, how many different arrangements are there?  
(3) If teachers and students alternate in the row, how many different arrangements are there?

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