
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
In a chess club election, 6 board member positions are open, and 20 candidates have been nominated, of which 10 are previous board members. Calculate the number of ways to elect the board such that at least one of the previous board members is elected.

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