
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 $f(x)=a(x-1)-2\ln{x}$ where $a\in\mathbb{R}$.
(I) Find the monotonic intervals of the function $f(x)$ when $a=1$.
(II) If the function $f(x)$ has no zero points in the interval $(0,1)$, find the range of $a$.

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