
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 the function $f(x)=\frac{1-x}{ax}+\ln x$.
(I) When $a=\frac{1}{2}$, find the maximum and minimum values of $f(x)$ on the interval $[1,e]$.
(II) If the function $g(x)=f(x)-\frac{1}{4}x$ is increasing on the interval $[1,e]$, find the range of values for the positive real number $a$.

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