
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 distinct numbers a and b are chosen randomly from the set $\{3, 3^2, 3^3, ..., 3^{15}\}$. What is the probability that $\mathrm{log}_a b$ is an integer?
A) $\frac{1}{10}$
B) $\frac{2}{7}$
C) $\frac{1}{7}$
D) $\frac{1}{5}$

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