
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
Point $P$ is a moving point on the curve $C_1: (x-2)^2 + y^2 = 4$. Using the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, establish a polar coordinate system. With the pole $O$ as the center, point $P$ is rotated counterclockwise by $90^\circ$ to obtain point $Q$. The trajectory equation of point $Q$ is denoted 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. Given the fixed point $M(2, 0)$, find the area of $\triangle MAB$.

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