
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 points A, B, and C lie on the graph of y=x^2, line AB is parallel to the x-axis, and triangle ABC is a right triangle with area 4032, find the sum of the digits of the y-coordinate of C, given that C also lies on the line x = 3 + y/4032.

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