
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 $(xOy)$, there is a line $C\_1$: $x + y = 1 + \sqrt{3}$, and a circle $C\_2$ with parametric equations $x = 2\cos\alpha$, $y = 2\sin\alpha$ ($\alpha$ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis.
(I) Find the polar coordinate equations for $C\_1$ and $C\_2$;
(II) Let points $A$ and $B$ be the intersections of line $C\_1$ and circle $C\_2$, with point $A$ being the midpoint of $OM$. Calculate the area of $\triangle OBM$.

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