
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 \( f(x)=\frac{\ln x}{x} \).

(1) Suppose there is a real number \( k \) such that \( f(x) < kx \) always holds. Find the range of \( k \).

(2) Let \( g(x)=f(x)-kx \) where \( k \in \mathbb{R} \). If the function \( g(x) \) has two zeros in the interval \(\left[\frac{1}{e}, e^{2}\right]\), find the range of \( k \).

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