
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 positive integers $a$ and $b$ (with $a>b$) is three times their geometric mean, what is a possible value for the ratio $a/b$, rounded to the nearest integer?
A) 30
B) 32
C) 34
D) 36
E) 38

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