
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 odd function defined on $(-\infty, 0) \cup (0, +\infty)$, and let $f'(x)$ be the derivative of $f(x)$. If $x > 0$, $x\ln x \cdot f'(x) + f(x) > 0$, then determine the range of values of $x$ that satisfy $\frac{{(x+2)f(x)}}{{x-1}} \leq 0$.

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