
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 a function $f(x)$ defined on $(0, +\infty)$, its derivative $f′(x)$ satisfies $$x^{2}f′(x) + 2xf(x) = \frac{\ln x}{x},$$ and $f(e) = \frac{1}{4e}$, where $e$ is the base of the natural logarithm. Find the solution set of the inequality $$f(x) + \frac{1}{x} > \frac{5}{4e}.$$

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