
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 two teachers, A and B, and four students standing in a row for a photo.
1. If teachers A and B must stand at the two ends, how many different arrangements are there?
2. If teachers A and B must stand next to each other, how many different arrangements are there?
3. If teachers A and B cannot stand next to each other, how many different arrangements are there?
4. If there must be two students standing between teachers A and B, how many different arrangements are there? (You must write the formula before calculating the result to receive credit)

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