
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 function $f(x)=\log_{a}x + \log_{\frac {1}{a}}8$ (where $a>0$ and $a\neq1$), if one number is randomly chosen to be $a$ from the set $\left\{\frac{1}{4}, \frac{1}{3}, \frac{1}{2}, 3, 4, 5, 6, 7\right\}$, find the probability that $f(3a+1) > f(2a) > 0$.

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