
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
In a class activity, 4 boys and 3 girls stand in a row to perform a program: (Write the necessary mathematical expressions, and answer with numbers)

(1) The three girls cannot stand next to each other. How many different standing arrangements are there?  
(2) The four boys stand next to each other. How many different arrangements are there?  
(3) Girl A cannot stand at the left end, and girl B cannot stand at the right end. How many different arrangements are there?  
(4) If A, B, and C are to stand in order from left to right according to their height (assuming their heights are all different), how many different arrangements are there?

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