
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 7 people standing in a row. How many different arrangements are there according to the following requirements?

(1) Among them, A cannot stand at the head, and B cannot stand at the tail;
(2) Among them, A, B, and C must stand next to each other;
(3) Among them, A, B, and C must not stand next to each other;
(4) There is exactly one person between A and B;
(5) A, B, and C must stand in order from left to right.

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