
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
Three girls and five boys stand in a row.  
(1) If the girls must stand together, how many different arrangements are there?  
(2) If the girls must be separated, how many different arrangements are there?  
(3) If girls cannot stand at either end, how many different arrangements are there?  
(4) If the boys stand in a fixed order, how many different arrangements are there?
(5) If the three girls stand in the front row and the five boys stand in the back row, how many different arrangements are there?

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