
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
Consider the equations $x^2 + kx + 12 = 0$ and $x^2 - kx + 12 = 0$. Suppose that each root of the second equation is $7$ more than the corresponding root of the first equation. Determine the value of $k$.
A) $3$
B) $-3$
C) $7$
D) $-7$

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