
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 the data set $x\_1$, $x\_2$, ..., $x\_n$ with a mean of $6$ and a standard deviation of $2$, find the mean and variance of the data set $2x\_1 - 6$, $2x\_2 - 6$, ..., $2x\_n - 6$.

A) $6$, $16$
B) $12$, $8$
C) $6$, $8$
D) $12$, $16$

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