
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 $f(x)$ has a domain of $(-2, 2)$, its derivative is $f'(x) = x^2 + 2\cos(x)$ and $f(0)=0$, find the range of real numbers $x$ such that $f(x-1)+f(x^2-x) > 0$.

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