
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 $y = x^2 + 3x - 4$ and the other two vertices at the intersections of the line $y = s$ with the parabola. Determine all possible values of $s$ such that the area of the triangle is exactly 24. Express your answer in interval notation.

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