
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
On Galactic Base Delta, Commander Xyrix has three new departmental heads needed: Chief of Security, Head of Logistics, and Chief Science Officer. Originally, 30 hopefuls submitted their applications. However, Commander Xyrix deemed only 15 of these candidates potential hires. How many different ways can Xyrix fill these positions assuming each candidate is eligible for one position only?

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