
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 $xOy$, there is a line $l_1: x=-2$, and a curve $$C: \begin{cases} x=2\cos\theta \\ y=2+2\sin\theta \end{cases}$$ (where $\theta$ is the parameter). A polar coordinate system is established with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis.
(1) Find the polar equations of line $l_1$ and curve $C$;
(2) If the polar equation of line $l_2$ is $$\theta= \frac {\pi}{4}$$ (where $\rho \in \mathbb{R}$), and assuming that the intersection points of $l_2$ and curve $C$ are $M$ and $N$, find the area of $\triangle CMN$ and the polar coordinates of the intersection point of $l_1$ and $l_2$.

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