
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 $f(x)$ ($x\neq 0$) is an even function and its derivative is $f′(x)$, it's known that $f(1)=0$ and $xf′(x) < 2f(x)$ when $x > 0$. Determine the range of $x$ values for which $f(x) > 0$.

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