
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 variance of the data \\({{x}\_{1}},{{x}\_{2}},\cdots,{{x}\_{n}}\\) is \\(3\\), if the variance of the data \\(a{{x}\_{1}}+b\\), \\(a{{x}\_{2}}+b\\), \\(\ldots\\), \\(a{{x}\_{n}}+b(a,b\in \mathbb{R})\\) is \\(12\\), then the value of \\(a\\) is.

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