
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, a group consisting of 4 boys and 2 girls stands in a row for a performance:  
(I) If the two girls cannot stand next to each other, how many different arrangements are there?  
(II) If girl A cannot stand at the left end and girl B cannot stand at the right end, how many different arrangements are there?  
(III) How many different arrangements are there if the 4 boys stand next to each other?  
(IV) How many different arrangements are there for A, B, and C to stand from left to right in order of height? (The heights of A, B, and C are all different)

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