
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 $xOy$, establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis, using the same unit of length in both coordinate systems. Given that circle $C$ has a center at point ($2$, $\frac{7π}{6}$) in the polar coordinate system and a radius of $\sqrt{3}$, and line $l$ has parametric equations $\begin{cases} x=- \frac{1}{2}t \\ y=-2+ \frac{\sqrt{3}}{2}t\end{cases}$.

(1) Find the Cartesian coordinate equations for circle $C$ and line $l$.
(2) If line $l$ intersects circle $C$ at points $M$ and $N$, find the area of triangle $MON$.

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