
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 $x_1, x_2, \ldots, x_n$ with a variance of 3, if the variance of the data $ax_1+b, ax_2+b, \ldots, ax_n+b$ ($a, b \in \mathbb{R}$) is 12, then all possible values of $a$ are \_\_\_\_\_\_.

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