
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
Two positive numbers, \( a \) and \( b \) (with \( a > b > 0 \)), have an arithmetic mean that is three times their geometric mean. What is the ratio \( \frac{a}{b} \) rounded to the nearest integer?
A) 28  
B) 30  
C) 32  
D) 34  
E) 36

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