
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 Math Club, after increasing its membership, now has 20 candidates nominated for 5 equal officer positions, of which 10 are past officers. How many possible elections of the officers will include at least one of the past officers?

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