
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 a function $f(x)$ with a domain of $(0,+\infty)$ satisfying that for any $x_{1}$, $x_{2} \in (0,+\infty)$ where $x_{1} \neq x_{2}$, $\frac{x_1f(x_2)-x_2f(x_1)}{x_2-x_1} > 1$, and $f(3) = 2$, determine the solution set of the inequality $f(x) < x-1$.

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