
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
In the Cartesian coordinate system $xOy$, the parametric equation of curve $C_1$ is $$\begin{cases} x=1+\cos\theta \\ y=2+\sin\theta\end{cases}$$ ($\theta$ is the parameter). Taking the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_2$ is $\rho\cos\theta=-2$.  
(I) Find the standard equations of $C_1$ and $C_2$ in the Cartesian coordinate system;  
(II) Given that the line $l: y=x$ intersects curve $C_1$ at points $M$ and $N$, find the polar coordinates of the midpoint of chord $MN$.

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