
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 functions $f(x)=a\ln x-x$ and $g(x)=x^{2}-(1-a)x-(2-a)\ln x$, where $a\in R$.
(1) Find the range of values of the real number $a$ for which $g(x)$ is an increasing function in its domain;
(2) If the graph of the function $F(x)=f(x)-g(x)$ intersects the $x$-axis at points $A$ and $B$, and the $x$-coordinate of the midpoint of $AB$ is $x_{0}$, can the tangent line to the function $F(x)$ at the point $(x_{0},F(x_{0}))$ be parallel to the $x$-axis?

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