
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
Assume the function $f(x) = \frac{1}{x\ln{x}}$ ($x > 0$ and $x \neq 1$),
(1) Determine the intervals over which the function $f(x)$ is monotonic;
(2) Given that $\frac{1}{x}\ln{2} > a \ln{x}$ holds true for any $x \in (0, 1)$, find the range of values for the real number $a$.

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