
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 equations \(x^2+kx+12=0\) and \(x^2-kx+12=0\). If, when the roots of the equations are suitably listed, each root of the second equation is \(3\) more than the corresponding root of the first equation, then \(k\) equals:
A) 2 B) 3 C) 4 D) 5 E) None of these

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