
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 average of a set of data $a_{1}$, $a_{2}$, $\ldots \ldots $, $a_{n}$ is $10$, and the variance is $4$, determine the average and variance of the data $2a_{1}+3$, $2a_{2}+3$, $\ldots $, $2a_{n}+3$.

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