
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 functions $f(x)=\ln x$ and $g(x)= \frac {k(x-1)}{x}$.
$(1)$ When $k=e$, find the monotonic intervals and extreme values of the function $h(x)=f(x)-g(x)$;
$(2)$ If $f(x) \geqslant g(x)$ always holds, find the value of the real number $k$.

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