
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
Let the function \( f^{\prime}(x) \) be the derivative of an even function \( f(x) \) with \( x \neq 0 \), and suppose \( f(-1)=0 \). Given that \( x f^{\prime}(x) - f(x) < 0 \) for \( x > 0 \), determine the range of \( x \) such that \( f(x) > 0 \).

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