
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 $f(x)$ is an even function defined on the domain $\{x|x\neq 0\}$, its derivative is $f′(x)$. For any positive real number $x$, it satisfies $xf′(x) > -2f(x)$. Determine the solution set for the inequality $g(x) < g(1)$, where $g(x)=x^{2}f(x)$.

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