
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 $f(x)=a\cdot{x}^{2}-(a+2)\cdot x+\ln x$.

(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 $f(x)$ has a minimum value of $-2$ on the interval $[1,e]$, find the range of $a$.

(III) If for any $x_{1}, x_{2} \in (0,+\infty)$, $x_{1} < x_{2}$, and $f(x_{1})+2x_{1} < f(x_{2})+2x_{2}$ always holds, find the range of $a$.

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