
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 $f(x)=x^{2}-(a+2)x+a\ln x$.
$(1)$ When $a=1$, find the extreme values of the function $f(x)$;
$(2)$ Let $y=g(x)$ be a function defined on $D$, and the equation of the tangent line at point $P(x_{0},y_{0})$ is $l$: $y=h(x)$. If for $x \neq x_{0}$, $\dfrac {g(x)-h(x)}{x-x_{0}} > 0$ always holds within $D$, then $P$ is called a "turning point" of the function $y=g(x)$. When $a=8$, does the function $y=f(x)$ have a "turning point"? If it exists, find the $x$-coordinate of the "turning point"; if not, please explain why.

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