
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 derivative of the even function $f(x) (x \neq 0)$ is $f'(x)$, and it satisfies $f(1) = 0$, when $x > 0$, $xf'(x) < 2f(x)$. Determine the range of $x$ that makes $f(x) > 0$ true.

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