
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 $f(x)=(2-a)(x-1)-2\ln x$ $(a\in \mathbb{R})$.

(Ⅰ) If the tangent line at the point $(1,g(1))$ on the curve $g(x)=f(x)+x$ passes through the point $(0,2)$, find the interval where the function $g(x)$ is decreasing;

(Ⅱ) If the function $y=f(x)$ has no zeros in the interval $\left(0, \frac{1}{2}\right)$, find the minimum value of $a$.

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