
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
Let the function $g(x)= \frac{{e}^{x}}{{x}^{2}}-t\left( \frac{2}{x}+\ln x\right)$ ($t$ is a constant, and $e$ is the base of the natural logarithm).

(I) If the graph of the function $g(x)$ passes through the point $(1,3e)$, find the expression for $g(x)$.

(II) When $t\leqslant 0$, find the extremum points of the function $g(x)$.

(III) If the function $g(x)$ has two extremum points in the interval $(0,2)$, find the range of values for $t$.

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