
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 Cartesian coordinate system $xOy$, the parametric equation of curve $C$ is $$\begin{cases} x=a+a\cos\beta \\ y=a\sin\beta \end{cases}$$ ($a>0$, $\beta$ is a parameter). Taking $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar equation of line $l$ is $\rho\cos(\theta- \frac{\pi}{3})= \frac{3}{2}$.  
(I) If curve $C$ and line $l$ have only one common point, find the value of $a$;  
(II) $A$ and $B$ are two points on curve $C$, and $\angle AOB= \frac{\pi}{3}$, find the maximum area of $\triangle OAB$.

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