
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. Calculate the minimum value of the variance of the new sample data.

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