
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 on $\mathbb{R}$, and for any $x_1, x_2 \in [0, +\infty)$ with $x_1 \neq x_2$, it holds that $(x_1 - x_2)[f(x_1)-f(x_2)] < 0$, find the relationship in magnitude among $f(-2)$, $f(0)$, and $f(3)$.

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