
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 \( y = 2x^2 - 4 \) and the other two vertices at the intersections of the line \( y = h \) with the parabola. Determine all possible values of \( h \) such that the area of the triangle is between \( 16 \) and \( 128 \) inclusive. Express your answer in interval notation.

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