
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. Let \( k \) be a real number such that \( f(x) < kx \) always holds. Determine the range of \( k \).
2. Let \( g(x) = f(x) - kx \) (where \( k \) is a real number). If the function \( g(x) \) has two zeros in the interval \(\left[\frac{1}{e}, e^{2}\right] \), determine the range of \( k \).

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