
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 $xOy$, the rectangular coordinate equation of circle $C$ is $(x- \sqrt {3})^{2}+(y-1)^{2}=4$. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of the $X$-axis as the polar axis.

1. Write the polar coordinate equation of circle $C$.
2. The polar coordinate equation of line $L$ is $θ= \frac {π}{3}$ ($ρ∈R$), which intersects with circle $C$ at points $M$ and $N$. Calculate the area of $△CMN$.

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