
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 of the sample $1+x_{1}$, $1+x_{2}$, $1+x_{3}$, …, $1+x_{n}$ is $10$, and the variance is $2$, determine the average and variance of the sample $2+x_{1}$, $2+x_{2}$, …, $2+x_{n}$.

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