
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), establish a rectangular coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The circle $C\_1$ is defined as $ρ^{2}-2 \sqrt {3}ρ\cos θ-4ρ\sin θ+6=0$.

1. Find the rectangular coordinate equation of circle $C\_1$ and the polar coordinate equation of line $l\_1$.
2. Let $M$, $N$ be the intersection points of $l\_1$ and $C\_1$. Calculate the area of $\triangle C\_1MN$.

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