
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 circle C is $$\begin{cases} x=cos\phi \ y=a+sin\phi \end{cases}$$ (a∈R, φ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the x-axis as the polar axis. The polar equation of the line is 2ρcos(θ+$$\frac{π}{6}$$) = 1, and the center of circle C is on the line l.
(I) Find the rectangular coordinate equation of line l and the polar coordinate equation of circle C.
(II) If A(ρ1, $$\frac{π}{6}$$) is a point on line l, and B(ρ2, $$\frac{4π}{3}$$) is a point on circle C, find the area of ΔOAB.

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