
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 4 boys and 3 girls standing in a row:
(1) If 3 people are selected to stand in a row, how many different arrangements are there?
(2) If boy A cannot stand at the head of the line, and girl B cannot stand at the end of the line, how many different arrangements are there?
(3) If the girls must stand together, how many different arrangements are there?
(4) If the 3 girls cannot stand next to each other, how many different arrangements are there?

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