
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 $8$ and their geometric mean is $15$, then an equation with the given two numbers as roots is:
A) \( x^2 - 16x + 225 = 0 \) \\
B) \( x^2 + 16x + 225 = 0 \) \\
C) \( x^2 - 32x + 225 = 0 \) \\
D) \( x^2 - 16x + 255 = 0 \) \\
E) \( x^2 - 8x + 225 = 0 \)

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