
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
Let point $P$ be a moving point on the curve $C\_1$: $(x-2)^2 + y^2 = 4$. 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. Rotate point $P$ counterclockwise by $90^{{∘}}$ around the pole $O$ to obtain point $Q$. Denote the trajectory equation of point $Q$ as curve $C\_2$.

1. Find the polar coordinate equations of curves $C\_1$ and $C\_2$.
2. The ray $\theta = \frac{\pi}{3} (\rho > 0)$ intersects curves $C\_1$ and $C\_2$ at points $A$ and $B$, respectively. Let $M(2,0)$ be a fixed point. Calculate the area of $\triangle MAB$.

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