
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
Let \\(k \in \mathbb{R}\\), and the function \\(f(x) = \ln x - kx\\).
- (I) If \\(k=1\\), determine the monotonicity of the function \\(y=f(x)\\) and find the extremum of the function;
- (II) If \\(f(x)\\) has no zeros, find the range of the real number \\(k\\).

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