
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 equations of the curve $C$ are given by $$\begin{cases} x=2+2\cos\alpha \\ y=2\sin\alpha \end{cases}$$ (where $\alpha$ is a parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive $z$-axis as the polar axis. The polar equation of line $l$ is given by $\rho\sin\left(\theta + \frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$.

(I) Find the Cartesian equation of curve $C$ and the polar equation of line $l$.
(II) Let point $M$ be located at $(0,1)$. If line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $|MA| + |MB|$.

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