
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 $f(x)=(x^{2}-2x)\ln x+ax^{2}+2$, $g(x)=f(x)-x-2$.

(Ⅰ) When $a=-1$, find the equation of the tangent line to $f(x)$ at $(1,f(1))$;

(Ⅱ) If $a > 0$ and the function $g(x)$ has exactly one zero, find the value of the real number $a$;

(Ⅲ) Under the condition of (Ⅱ), if $e^{-2} < x < e$ and $g(x) \leqslant m$ always holds, find the range of the real number $m$.

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