
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 $f(x) = x^{2} + \frac{2}{x} + a\ln x$, where $a \in \mathbb{R}$,

(I) If $a = -4$, determine the intervals of monotonicity of $f(x)$.
(II) If the function $f(x)$ is strictly increasing on the interval $[1, +\infty)$, find the range of the real number $a$.
(III) Define the function $g(x) = x^{2}f'(x)$. If the minimum value of $g(x)$ is $-6$, find the explicit expression of $f(x)$.

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