
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
Elective 4-4 Coordinate System and Parametric Equations  
In the plane Cartesian coordinate system, take the origin as the pole and the positive half-axis of the x-axis as the polar axis to establish the polar coordinate system. It is known that the polar equation of curve $C_1$ is: $\rho=2\cos\theta$, and the parametric equation of line $C_2$ is: $$\begin{cases} \left.\begin{matrix}x=1+ \frac { \sqrt {2}}{2}t \\ y=3+ \frac { \sqrt {2}}{2}t\end{matrix}\right.\end{cases}$$ (t is the parameter)  
(I) Find the Cartesian coordinate equation of curve $C_1$ and the general equation of line $C_2$.  
(II) First, move all points on curve $C_1$ to the left by 1 unit length, then stretch the x-coordinates of all points on the graph by $\sqrt {3}$ times to get curve $C_3$. Let P be a moving point on curve $C_3$, find the minimum distance from point P to line $C_2$, and find the coordinates of point P at that time.

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