
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
A club has 25 members and needs to select 4 officers: president, secretary, treasurer, and spokesperson. Each person can hold at most one office. Three of the members, Alice, Bob, and Carol, insist on the condition that either all three are officers or none of them are. How many ways can the club select its officers under this condition?

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