
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 in the Cartesian coordinate system, the parametric equations of curve C are $$\begin{cases} x=1+2\cos\varphi \\ y=1+2\sin\varphi\end{cases}$$ (where $\varphi$ is the parameter). Now, establishing a polar coordinate system with the origin as the pole and the positive half-axis of x as the polar axis, the polar equation of line $l$ is $\rho= \frac {4}{\cos\theta-\sin\theta}$.  
(1) Find the general equation of curve C and the Cartesian equation of line $l$;  
(2) Does there exist a point P on curve C such that the distance from point P to line $l$ is minimized? If it exists, find the minimum distance and the Cartesian coordinates of point P; if not, please explain why.

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