
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 function $f(x)$ is defined on $(0, +\infty)$, and $f(2)=0$. Also, for $0 < x_1 < x_2$, it holds that $$\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}} > 0$$. Then, the solution set of the inequality $f(x) < 0$ is \_\_\_\_\_\_.

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