
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 $f(x)=ax^{2}-(a+2)x+\ln x$.
(I) When $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$;
(II) When $a > 0$, if the minimum value of $f(x)$ on the interval $[1,e]$ is $-2$, find the range of values for $a$;
(III) If for any $x_{1}$, $x_{2}\in(0,+\infty)$, when $x_{1}\neq x_{2}$, we have $\frac{f(x_{1})+2x_{1}-[f(x_{2})+2x_{2}]}{x_{1}-x_{2}} > 0$ always holds, find the range of values for $a$.

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