
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 data $x_{1}$, $x_{2}$, …, $x_{n}$ with a variance of $3$, if the variance of the data $ax_{1}+b$, $ax_{2}+b$, …, $ax_{n}+b$ $(a,b \in \mathbb{R})$ is $12$, then all the values of $a$ are ______.

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