
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]


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In the Cartesian coordinate system $xOy$, the general equation of circle $C$ is $x^{2}+y^{2}-4x-6y+12=0$. In the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the polar equation of line $l$ is $\rho\sin (\theta+ \frac {\pi}{4})= \sqrt {2}$.  
(Ⅰ) Write the parametric equation of circle $C$ and the Cartesian equation of line $l$;  
(Ⅱ) Suppose the intersection points of line $l$ with the $x$-axis and $y$-axis are $A$ and $B$ respectively, and $P$ is any point on circle $C$. Find the range of values for $\overrightarrow{PA}\cdot \overrightarrow{PB}$.

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