
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
Given that a set of $n$ people participate in an online video soccer tournament, the statistics from the tournament reveal: The average number of complete teams wholly contained within randomly chosen subsets of $10$ members equals twice the average number of complete teams found within randomly chosen subsets of $7$ members. Find out how many possible values for $n$, where $10\leq n\leq 2017$, satisfy this condition.

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