
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 $f(x)=2\ln x-(x-1)^{2}-2k(x-1)$.  
(I) When $k=1$, find the intervals of monotonicity and the extremum of $f(x)$.  
(II) Determine the range of the real number $k$ such that there exists $x_{0} > 1$, for $x\in(1,x_{0})$, $f(x) > 0$ always holds.

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