
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 that the arithmetic mean of two positive numbers \(a\) and \(b\) (with \(a > b > 0\)) is three times their geometric mean, find the closest integer value for the ratio \( \frac{a}{b} \).
A) 32
B) 33
C) 34
D) 35
E) 36

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