
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 $f(x)=(2-a)(x-1)-2\ln x$,
(1) Find the monotonic intervals of $f(x)$ when $a=1$;
(2) Find the minimum value of $a$ such that the function $f(x)$ has no zeros on $(0, \frac{1}{2})$.

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