
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 $f′(x)$, and it satisfies the equation $xf′(x)+2f(x)= \frac{\ln x}{x}$, with $f(e)= \frac{1}{2e}$.

(I) Find the expression for $f(x)$.
(II) Find the maximum and minimum values of the function $f(x)$ on the interval $[1,e^{2}]$.

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