
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 mean and variance of the sample data $x_{1}$, $x_{2}$, ..., $x_{10}$ are $3$ and $5$ respectively, if $y_{i}=x_{i}+a$ ($a$ is a non-zero real number, $i=1$, $2$, ..., $10$), determine the mean and variance of $y_{1}$, $y_{2}$, ..., $y_{10}$.

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