
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 an even function $f(x)$ with the domain $\{x|x\neq 0\}$ and its derivative $f'(x)$, for any positive real number $x$, it satisfies $xf'(x) > -2f(x)$. If $g(x) = x^2f(x)$, determine the solution set of the inequality $g(x) < g(1-x)$.

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