
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]


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If the function $f(x)$ defined on $(-\infty, 0) \cup (0, +\infty)$ satisfies the following conditions: ① $f(x)$ is an even function; ② For any $x_{1}, x_{2} \in (0, +\infty)$, with $x_{1} \neq x_{2}$, $\frac{{x}_{2}^{2}f({x}_{1})-{x}_{1}^{2}f({x}_{2})}{{x}_{1}-{x}_{2}}＜0$, then the function $f(x)$ is said to have property $P$. Given that the function $f(x)$ has property $P$, the solution set of the inequality $f(x-2)＜\frac{f({x}^{2}-4)}{(x+2)^{2}}$ is ______.

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