
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
Let the function $f(x)=(x-a)^{2}$ where $a\in\mathbb{R}$, and $g(x)=\ln x$,

(I) Try to find the number of common points between the tangent line $l$ at point $(1,F(1))$ and the curve $F(x)=f(x)+g(x)$;

(II) If the function $G(x)=f(x)\cdot g(x)$ has two extreme points, find the range of the real number $a$.

(Note: When $a < 0$, as $x$ approaches $0$, $2\ln x- \frac{a}{x}$ tends to $+\infty$)

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