
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 $f(x)$ is an odd function defined on $(-\infty, 0) \cup (0, +\infty)$, and $f'(x)$ is the derivative of $f(x)$. When $x > 0$, $xf'(x) + 2f(x) > 0$. If $f(2) = 0$, find the solution set of the inequality $x^{3}f(x) > 0$.

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