
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
Let $A$, $B$, and $C$ be three distinct points on the graph of $y=x^2$. Assume line $AB$ is horizontal at $y=25$ and $\triangle ABC$ is an isosceles right triangle with area $500$. Determine the sum of the digits of the $y$-coordinate of point $C$.
A) 6
B) 7
C) 8
D) 9
E) 10

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