
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
Vertex $A$ of $\bigtriangleup ABC$ is at the origin of a coordinate system where vertices $B$ and $C$ lie on the parabola defined by $y = -x^2$. The line segment $\overline{BC}$ is parallel to the $x$-axis. The area of $\triangle ABC$ is $72$. Determine the length of $BC$.
A) $12$  
B) $12\sqrt[3]{2}$  
C) $12\sqrt[3]{\frac{1}{2}}$  
D) $12\sqrt[3]{\frac{1}{3}}$  
E) $18$

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