
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
At the end of the year, the Art Club decided to hold an election where 6 equivalent officer positions were available. A total of 18 candidates were nominated for these positions, of whom 8 were past officers. Determine how many possible elections of the officers would include at least one of the past officers.

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