
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
Consider a triangle $\bigtriangleup PQR$ where all three vertices lie on the curve defined by $y = 2x^2$. Vertex $P$ is at the origin, and line segment $\overline{QR}$ is parallel to the $x$-axis. The area of the triangle is $128$ square units. Find the length of $\overline{QR}$.
A) 6  
B) 8  
C) 10  
D) 16  
E) 18

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