
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
Define a function $f(x)$ on $(0, +\infty)$ that satisfies: $$\frac {x_{1}f(x_{1})-x_{2}f(x_{2})}{x_{1}-x_{2}} < 0,$$ and $f(2) = 4$. Then, determine the solution set of the inequality $f(x) - \frac {8}{x} > 0$.

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