
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 mean of the data $x_1, x_2, \ldots, x_n$ is $\overline{x}$, and the variance is $S^2$, calculate the mean and variance of $2x_1+3, 2x_2+3, \ldots, 2x_n+3$.

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