
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 odd function $f(x)$ and the even function $g(x)$ have the domain $(-\infty, 0) \cup (0, +\infty)$, and when $x < 0$, $f'(x)g(x) + f(x)g'(x) > 0$. If $g(-2) = 0$, then the solution set of the inequality $f(x)g(x) > 0$ is.

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