
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 the set of real numbers $\mathbb{R}$, $\forall x\_1 \geqslant 0$, $\forall x\_2 \geqslant 0$, if $x\_1 \neq x\_2$, then $\frac{f(x\_2) - f(x\_1)}{x\_2 - x\_1} < 0$. If $f(\frac{1}{3}) = \frac{3}{4}$ and $4f(\log_{\frac{1}{8}}x) > 3$, find the range of $x$.

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