
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 $g\left(x\right)=\dfrac{2}{x}-a\ln x\left(a\in R\right)$, $f\left(x\right)=x^{2}+g\left(x\right)$:
- (Ⅰ) Find the monotonic interval of the function $g\left(x\right)$;
- (Ⅱ) If $f\left(x\right)$ has extreme values in the interval $\left(0,1\right)$, find the range of $a$;
- (Ⅲ) When $a \gt 0$, if $f\left(x\right)$ has a unique zero point $x_{0}$, find $\left[x_{0}\right]$.
(Note: $\left[x\right]$ denotes the floor function, representing the largest integer not exceeding $x$, such as $\left[0.3\right]=0$, $\left[2.6\right]=2$, $\left[-1.4\right]=-2$; Reference values: $\ln 2=0.6931, \ln 3=1.099, \ln 5=1.609, \ln 7=1.946)$

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