
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
Let $f(x)$ be an odd function defined on $\mathbb{R}$, with $f(-2) = 0$. If for any two distinct positive numbers $x_{1}$ and $x_{2}$, $\frac{x_{2}f(x_{1}) - x_{1}f(x_{2})}{x_{1} - x_{2}} < 0$, then the solution set of the inequality $\frac{f(x)}{x} < 0$ is ____.

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