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

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