
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
Assume a triangle is formed with one vertex at the vertex of the parabola $y=x^2 + 2$ and the other two vertices at the intersections of the line $y=mx + c$ with the parabola, where $m$ is the slope of the line, and $c$ is the y-intercept. If the area of the triangle is exactly 12, find all possible values of $m$ when $c=1$. Express your answer in an interval or list format.

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