
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 $f(x), g(x)$ are an odd function and an even function defined on $R$ respectively, with $f(-3) = 0$, and $f'(x)g(x) < f(x)g'(x)$ when $x < 0$, determine the solution set of $\frac{f(x)}{g(x)} < 0$.

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