
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
Given the parabola $y=x^2 + 1$ and triangle $\bigtriangleup ABC$ with vertex $A$ at the origin, where $\overline{BC}$ is parallel to the $x$-axis and steps up along $y$ every unit in $x$, determine the length of $\overline{BC}$ such that the area of the triangle is $100$.

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