
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 $y=f(x)$ ($x \in \mathbb{R}$) has a derivative denoted by $f'(x)$. If $f(x)-f(-x)=2x^{3}$, and when $x \geqslant 0$, $f'(x) > 3x^{2}$, determine the solution set of the inequality $f(x)-f(x-1) > 3x^{2}-3x+1$.

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