
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 $f\left( x \right)=\left( 2-a \right)\left( x-1 \right)-2\ln x\ (a\ is\ a\ constant)$

(1) When $a=1$, find the monotonic intervals of $f(x)$;

(2) If the function $y=f\left( x \right)$, $x\in(0,\frac{1}{2})$ has no points intersecting with the $x$ axis, find the minimum value of the real number $a$.

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