
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 5 girls, all lined up in a row. How many different arrangements are there for the following situations?

(I) A is neither in the middle nor at the ends;  
(II) A and B must be placed at the ends;  
(III) Boys and girls are grouped together;  
(IV) Boys and girls alternate;  
(V) A, B, and C are in a fixed order from left to right.

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