
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 $f(x)=2x+\frac{2}{x}-alnx$, where $a\in R$.  
$(1)$ If the function $f(x)$ is monotonically increasing on $\left[1,+\infty \right)$, find the range of real number $a$.  
$(2)$ Let $g(x)=x^{2}\left[f'(x)+2x-2\right]$. If the minimum value of $g(x)$ is $-6$, find the value of $a$.

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