
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
A group of 4 teachers and 4 students are lined up for a photo.
(I) If the 4 students must stand together, how many different arrangements are there?
(II) If no two students can stand next to each other, how many different arrangements are there?
(III) If the teachers and students stand alternately, how many different arrangements are there? Please answer with numerical values.

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