
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 $y=4x^2$. The vertex $A$ is at the origin and $\overline{BC}$ is parallel to the $x$-axis. $B$ and $C$ are placed at $x = -b$ and $x = c$ respectively, where $b>0$ and $c>0$. The area of the triangle is $96$. What is the length of $BC$?
**A)** $\frac{50}{9}$, **B)** $\frac{55}{9}$, **C)** $\frac{59}{9}$, **D)** $\frac{64}{9}$, **E)** $\frac{68}{9}$

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