
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
If the mean of the data $X_{1}$, $X_{2}$, ..., $X_{n}$ is $\overline{x}$, and the variance is $S^{2}$, determine the mean and variance of $2X_{1}+3$, $2X_{2}+3$, ..., $2X_{n}+3$.

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