
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
8 girls and 25 boys are seated in a circle such that there are at least two boys between any two girls. How many different arrangements are possible (arrangements that can be obtained by rotating the circle are considered the same)?

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