
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 equations of the curve $C$ are $$\begin{cases} x=4\cos\alpha \\ y=4\sin\alpha \end{cases}$$ (where $\alpha$ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar coordinate equation of line $l$ is $\rho\cos\left(\theta - \frac{\pi}{3}\right) = 2$.
(I) Find the Cartesian equation of curve $C$ and the rectangular coordinate equation of line $l$.
(II) Let line $l$ intersect the $x$-axis and $y$-axis at points $A$ and $B$, respectively, and let point $M$ be on curve $C$. Find the maximum area of triangle $MAB$.

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