
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
(The full score for this question is 10 points)

There are 7 students standing in a row. How many different arrangements are there for each of the following situations?

(1) A and B must stand together;

(2) A is not at the head of the line, and B is not at the end of the line;

(3) A and B must not stand next to each other;

(4) There must be one person standing between A and B.

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