
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 $x_{1}+1$, $x_{2}+1$, $\ldots$, $x_{n}+1$ is $17$, and the variance is $2$, then the average and variance of another set of data $x_{1}+2$, $x_{2}+2$, $\ldots$, $x_{n}+2$ are _____ and _____, respectively.

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