
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 that the points $(8,3)$ and $(-3,6)$ are on the graph of the function $f(x)=\begin{cases}\log_{a}x, & x > 0 \\ b^{x}-2, & x\leqslant 0\end{cases}$.

$(1)$ Find the explicit formula for the function $f(x)$;

$(2)$ Find the solution set for the inequality $f(x) > 0$.

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