
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 $f(x)=\frac{x}{\ln x}-ax (x > 0, x \neq 1)$.
(1) Find the minimum value of the real number $a$ such that the function $f(x)$ is a decreasing function on $(1,+\infty)$.
(2) Find the range of values of the real number $a$ such that there exist $x\_1, x\_2 \in [e, e^2]$ that satisfy $f(x\_1) \leq f'(x\_2)+a$.

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