
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 $xOy$, the parametric equation of the curve $C_1$ is given by $\begin{cases} x=\cos\alpha \\ y=1+\sin\alpha \end{cases}$ (where $\alpha$ is the parameter). Point $P$ moves on curve $C_1$, and line segment $OP$ is rotated counterclockwise by 90° around point $O$ to obtain line segment $OQ$. The locus of point $Q$ is curve $C_2$. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive $x$-axis as the polar axis.
(I) Find the polar equations of curves $C_1$ and $C_2$;
(II) Under the conditions of (I), if the ray $\theta=\frac{\pi}{3}$ ($\rho\geq 0$) intersects curves $C_1$ and $C_2$ at points $A$ and $B$ respectively (excluding the pole), and there is a fixed point $M(4,0)$, find the area of triangle $MAB$.

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