
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 $xOy$, consider the line $l: y=x$ and the circle $C: \begin{cases} x=-1+\cos \varphi \\ y=-2+\sin \varphi \end{cases} (\varphi$ is a parameter), with the origin as the pole and the positive half-axis of $x$ as the polar axis to establish the polar coordinate system.  
(Ⅰ) Find the polar equations of line $l$ and circle $C$;  
(Ⅱ) Suppose the intersection points of line $l$ and circle $C$ are $M$ and $N$, calculate the area of $\triangle CMN$.

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