
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 $y=2x^2$, let $A$, $B$, and $C$ be three distinct points on the graph such that line $AB$ is parallel to the $x$-axis and $\triangle ABC$ is a right triangle with area $1024$. Find the sum of the digits of the $y$-coordinate of $C$.

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