
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 $C_1$ are given by $\begin{cases} x=2+rcos\alpha \\ y=rsin\alpha \end{cases}$ (where $\alpha$ is the parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of the curve $C_2$ is given by $ρsin(θ+ \frac {π}{6})=3$, and the curves $C_1$ and $C_2$ intersect at exactly one point.
(I) Find the polar equation of the curve $C_1$;
(II) Given two points, $A$ and $B$, on the curve $C_1$ such that $∠AOB= \frac {π}{4}$, find the maximum area of $\triangle AOB$.

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