
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
Let $f(x)$ be an even function that is increasing on $(0,+\infty)$. If $x\_1 < 0$, $x\_2 > 0$, and $|x\_1| > |x\_2|$, determine the relationship between $f(x\_1)$ and $f(x\_2)$.

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