
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 large debate club has 30 members. The club needs to elect 5 positions: president, vice president, secretary, treasurer, and public relations officer. Each person can hold at most one role. Four of the members, Alice, Bob, Carol, and Dave, have a specific condition: either all four are positioned, or none are. In how many ways can the club elect its officers given these constraints?

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