
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 standard deviation of the sample $x_{1}$, $x_{2}$, $\cdots$, $x_{n}$ is $0.1$, if $y_{i}=1-2x_{i}$ $(i=1,2,\cdots,n)$, then the standard deviation of the sample $y_{1}$, $y_{2}$, $\cdots$, $y_{n}$ is ______.

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