
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
A set S is defined as $\{3, 3^2, 3^3, ..., 3^{18}\}$. Two distinct numbers a and b are chosen randomly from S. What is the probability that $\mathrm{log}_a b$ is an integer?
A) $\frac{17}{153}$
B) $\frac{23}{153}$
C) $\frac{32}{153}$
D) $\frac{40}{153}$
E) $\frac{50}{153}$

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