
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
A triangle is formed with one vertex at the vertex of the parabola \(y=x^2+3\) and the other two vertices at the intersections of the line \(y=r\) and the parabola. If the area of the triangle is between 12 and 48 inclusive, find all possible values of \(r\). Express your answer in interval notation.

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