
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
Seven students are lining up for a photo.

(1) If they are divided into two rows for the photo, with 3 people in the front row and 4 people in the back row, how many different arrangements are there?

(2) If they are arranged into two rows for the photo, with 3 people in the front row and 4 people in the back row, but with the condition that person A must be in the front row and person B must be in the back row, how many different arrangements are there?

(3) If they are arranged in a single row for the photo, and persons A, B, and C must be next to each other, how many different arrangements are there?

(4) If they are arranged in a single row for the photo, among the 7 people there are 4 boys and 3 girls, and the girls cannot be next to each other, how many different arrangements are there?

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