
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 3 officers: a president, a secretary, and a treasurer. Each person can hold at most one office. Three of the members, Alice, Bob, and Charlie, will only be officers if at least one of the other two is also an officer. In how many ways can the club choose its officers?

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