
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 a set of numbers $x_{1}$, $x_{2}$, ..., $x_{n}$ with mean $\bar{x}$ and standard deviation $s$, calculate the mean and standard deviation of the set of numbers $2x_{1}+1$, $2x_{2}+1$, ..., $2x_{n}+1$.

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