
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 the sample data $x_1, x_2, \ldots, x_{10}$ with a mean of 2 and a variance of 5, if $y_i = x_i + a$ (where $a$ is a non-zero real number, $i=1,2,\ldots,10$), calculate the mean and variance of $y_1, y_2, \ldots, y_{10}$.

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