
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 2 girls standing in a row. How many arrangements are there for each of the following situations?  
(I) Boy A does not stand at the head or the tail of the row.  
(II) The two girls must stand next to each other.  
(III) Students A, B, and C are not next to each other.  
(IV) A does not stand at the head, and B does not stand at the tail.

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