
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 $f(x)=a\ln x+bx\ (a,b\in \mathbb{R})$, $g(x)=\frac{1}{2}x^{2}-(m+\frac{1}{m})x\ (m > 0)$, and the tangent line of $y=f(x)$ at the point $(1,f(1))$ is $x-y-1=0$.

(Ⅰ) Find the values of $a$ and $b$;  
(Ⅱ) If the function $h(x)=f(x)+g(x)$ has exactly one extreme point in the interval $(0,2)$, find the range of $m$.

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