
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 $f(x)=2x+ \frac {2}{x}+a\ln x,a∈R$.
(1) If the function $f(x)$ is monotonically increasing on $[1,+∞)$, find the range of values for the real number $a$.
(2) Let the function $g(x)=x^{2}[f′(x)+2x-2]$, if the minimum value of $g(x)$ is $(-6)$, find the analytic expression of the function $f(x)$.

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