
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 rectangular coordinate system $(xOy)$, there is a line $l_{1}$: $x=-2$, and a curve $C$: $\begin{cases} x=2\cos \theta \\ y=2+2\sin \theta \end{cases}(\theta$ is a parameter$)$. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive half of the $x$-axis as the polar axis.
(1) Find the polar coordinate equations of the line $l_{1}$ and the curve $C$;
(2) If the polar coordinate equation of line $l_{2}$ is $\theta= \frac {\pi}{4}(\rho\in R)$, let the intersection points of $l_{2}$ and curve $C$ be $M$, $N$, 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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