
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
The Astronomy Club at a school has 25 members. It needs to elect 3 officers: president, secretary, and treasurer. No person can hold more than one office. Two of the members, Rachel and Simon, will only serve as officers if the other is also an officer. Additionally, another pair, Penelope and Quentin, also will only serve together. In what ways can the club choose its officers?

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