
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
Determine the value of $c$ in the equation $y = x^2 - 10x + c$ such that the vertex of the parabola is located exactly 10 units from the origin.
**A)** $25+5\sqrt{2}$
**B)** $25+5\sqrt{3}$
**C)** $25-5\sqrt{2}$
**D)** $25-5\sqrt{3}$
**E)** $50$

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