
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 the function $f(x)$ defined on $\{x | x \neq 0\}$ that satisfies $f(x) - f(-x) = 0$, if the derivative of $f(x)$ is $f'(x)$ and $f(1) = 0$, and for $x > 0$, it holds that $xf''(x) < 2f(x)$, determine the solution set where the inequality $f(x) > 0$ is true.

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