
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 an even function defined on $R$, for any $x_{1}$, $x_{2} \in [0, +\infty)$, and $x_{1} \neq x_{2}$, we have $\frac{f(x_{1}) - f(x_{2})}{x_{1} - x_{2}} > 0$. If $f(1) = 0$, find the solution set of the inequality $(x-1)f(x) > 0$.

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