
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 $(-\infty, +\infty)$, for any $x_1$, $x_2\in [0,+\infty)$ $(x_1\neq x_2)$, we have $\frac{f(x_2)-f(x_1)}{x_2-x_1} < 0$. Determine the correct order of the function values $f(3)$, $f(1)$, and $f(-2)$.

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