
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 students, consisting of 4 boys and 3 girls, standing in a line from front to back.  
(1) How many different arrangements are there?  
(2) If student A cannot stand at the front, how many different arrangements are there?  
(3) If the three girls must not stand next to each other, how many different arrangements are there?  
(4) If the three girls must stand in order from tallest to shortest from front to back, how many different arrangements are there?  
(5) If the three girls must stand together, how many different arrangements are there?

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