
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 that the average and variance of sample data $x_{1}$, $x_{2}$, $\ldots$, $x_{2022}$ are $3$ and $56$ respectively, and $y_{i}=2x_{i}+3$ $(i=1,2,\ldots,2022)$, calculate the average and variance of $y_{1}$, $y_{2}$, $\ldots$, $y_{2022}$.

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