
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 the set $A=\{2,3,4,8,9,16\}$, if $a\in A$ and $b\in A$, the probability that the event "$\log_{a}b$ is not an integer but $\frac{b}{a}$ is an integer" occurs is $\_\_\_\_\_\_$.

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