
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 even function f(x) is defined on the domain $(-\infty, 0) \cup (0, +\infty)$, its derivative is f'(x), and $2f(x) + xf'(x) > 0$ holds for any x in the domain, find the solution set of the inequality $x^2 f(x) < 4$.

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