
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 numbers $x_1, x_2, …, x_n$ with mean $\overline{x}$ and variance $s^2$, find the mean and variance of another set of numbers $\sqrt{3}x_1+ \sqrt{2}, \sqrt{3}x_2+ \sqrt{2}, …, \sqrt{3}x_n+ \sqrt{2}$.

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