
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
All three vertices of $\bigtriangleup ABC$ lie on the parabola defined by $y = 2x^2$, with $A$ at the origin and $\overline{BC}$ horizontal. The area of the triangle is $72$. What is the length of $BC$?
**A)** $2 \times \sqrt[3]{18}$
**B)** $2 \times \sqrt[3]{24}$
**C)** $2 \times \sqrt[3]{36}$
**D)** $4 \times \sqrt[3]{9}$
**E)** $2 \times \sqrt[3]{48}$

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