
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 domain of the function $y=f(x)$ is $R$, $f(x)$ is an even function, and for any $x_{1}$, $x_{2} \in (-\infty, 0]$, $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} > 0$. If $f(6) = 1$, determine the solution to the inequality $f(x^{2}-x) > 1$.

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