
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 the derivative of the function $f(x)$ is $f′(x)$, $e$ is the base of the natural logarithm, and the function $f(x)$ satisfies $xf′(x)+f(x)= \frac{\ln x}{x}$, with $f(e)= \frac{1}{e}$, determine the solution set of the inequality $f(x)-x > \frac{1}{e}-e$.

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