
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
Given the line $l_{1}$: $\begin{cases} x=t \\ y= \sqrt {3}t \end{cases}$ (where $t$ is a parameter), and the circle $C_{1}$: $(x- \sqrt {3})^{2}+(y-2)^{2}=1$, with the origin as the pole and the positive half-axis of $x$ as the polar axis to establish a Cartesian coordinate system.  
$(1)$ Find the polar equation of the circle $C_{1}$ and the polar equation of the line $l_{1}$.  
$(2)$ Let the intersection points of $l_{1}$ and $C_{1}$ be $M$ and $N$, find the area of $\triangle C_{1}MN$.

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