
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. (You must write down the formula before calculating the result to score points)  
(Ⅰ) If the 3 girls must stand together, how many different arrangements are there?  
(Ⅱ) If no two girls are next to each other, how many different arrangements are there?  
(Ⅲ) If there are exactly three people between person A and person B, how many different arrangements are there?

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