
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 the function $f(x)=x^{3}-6x+5$, where $x\in\mathbb{R}$.  
(I) Find the extreme points of $f(x)$.  
(II) Given that when $x\in(1,+\infty)$, $f(x)\geqslant k(x-1)$ always holds, find the range of the real number $k$.

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