
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 to perform:
(I) The two girls cannot stand next to each other. How many different arrangements are possible?
(II) Girl A cannot stand at the left end, and Girl B cannot stand at the right end. How many different arrangements are possible?
(III) How many different arrangements are possible if the 4 boys must stand next to each other?
(IV) In how many different ways can A, B, and C stand from left to right in order of height? (Assuming A, B, and C each have different heights)

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