
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 high school's advanced mathematics study group for the class of 2010 consists of 3 boys and 2 girls, making a total of 5 students who stand in a row for a photo.
(1) How many different arrangements are there if two specific students, A and B, must stand next to each other?
(2) How many different arrangements are there if two specific students, A and B, must not stand next to each other?
(3) How many different arrangements are there if student A cannot stand at the far left and student B cannot stand at the far right?

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