
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 a set of sample data with $8$ numbers, the average is $8$, and the variance is $12$. Two unknown numbers are added to this set of sample data to form a new set of sample data. It is known that the average of the new sample data is $9$. Find the minimum value of the variance of the new sample data.

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