
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 $f(x)$ defined on $R$ satisfies $(x\_1-x\_2)[f(x\_1)-f(x\_2)] > 0$ for all $x\_1$, $x\_2\in[0,+\infty)$, determine the relationship among $f(-2)$, $f(1)$, and $f( \frac {1}{2})$.

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