
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
If the arithmetic mean of two numbers is $10$ and their geometric mean is $24$, then an equation with the given two numbers as roots is:
A) $x^2 - 20x + 475 = 0$
B) $x^2 - 20x + 576 = 0$
C) $x^2 + 22x - 476 = 0$
D) $x^2 - 22x + 576 = 0$
E) $x^2 - 20x + 600 = 0$

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