
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 $f(x)=(x^{2}-2x) \ln x+a x^{2}+2$, and $g(x)=f(x)-x-2$.
(I) When $a=-1$, find the equation of the tangent line to $f(x)$ at the point $(1,f(1))$;
(II) If $a > 0$ and the function $g(x)$ has exactly one zero, find the value of the real number $a$;
(III) Under the conditions of (II), if $e^{-2} < x < e$ and $g(x)\leqslant m$ is always true, find the range of values for the real number $m$.

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