
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 $f(x)=x^{2}+ax-\ln x$, where $a\in\mathbb{R}$.
(I) If $a=0$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$;
(II) If the function $f(x)$ is decreasing on the interval $[1,2]$, find the range of values for the real number $a$;
(III) Let $g(x)=f(x)-x^{2}$. Determine if there exists a real number $a$ such that the minimum value of the function $g(x)$ is $3$ when $x\in(0,e]$ ($e$ is the natural constant). If it exists, find the value of $a$; if not, explain the reason.

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