
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
3 girls and 5 boys are lined up in a row.  
(Ⅰ) If the girls must all be together, how many different arrangements are possible?  
(Ⅱ) If the girls must all be separated, how many different arrangements are possible?  
(Ⅲ) If girls cannot be placed at both ends, how many different arrangements are possible?  
(Ⅳ) If girls cannot be placed at both ends simultaneously, how many different arrangements are possible?

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