
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 $\triangle ABC$ lie on the parabola defined by $y=x^2 + 1$, with $A$ at $(0,1)$ and $\overline{BC}$ parallel to the line $y = x$. The area of the triangle is $32$. What is the length of $\overline{BC}$?
A) 6
B) 8
C) 10
D) 12
E) 16

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