
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
Six people are taking a photo.
(1) They stand in a row with persons A and B next to each other. How many different arrangements are possible?
(2) They stand in a row with person A not at the head and person B not at the tail. How many different arrangements are possible?
(3) They stand in two rows with three people per row, and the front row is shorter than the back row. How many different arrangements are possible?

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