
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
How many different ways can 7 people be arranged in a row under the following conditions?
(1) Person A is at the head of the row;
(2) Person A, Person B, and Person C must be together;
(3) Persons A, B, and C must not be next to each other;
(4) Person A is not at the head of the row, and Person B is not in the middle.

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