
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 sample data $x_{1}$, $x_{2}$, $\ldots $, $x_{n}$ is $10$, and the variance of another set of sample data $2x_{1}+4$, $2x_{2}+4$, $\ldots $, $2x_{n}+4$ is $8$, find the average and variance of the combined set of sample data.

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