
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 $f(x)=\ln x$ and $g(x)=\frac{1}{2}x^{2}-kx$:

1. If $k=m+\frac{1}{m}$ ($m>0$) and the function $h(x)=f(x)+g(x)$ has exactly one extreme value in the interval $(0,2)$, find the range of real number $m$.
2. If the function $M(x)=f(x)-g(x)$ has two zero points $x\_1$ and $x\_2$ ($x\_1>x\_2$) that satisfy $2x\_0=x\_1+x\_2$, can the tangent line of $M(x)$ at $(x\_0,M(x\_0))$ be parallel to the line $y=1$? If so, find the equation of the tangent line. If not, explain why.

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