
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 annual Chess Club election, 20 candidates are nominated for 6 officer positions. Among the candidates, 8 have previously served as officers. Calculate the number of ways to elect the officers such that at least one past officer is included.

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