
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 C₁ are $$\begin{cases} x=2+2\cos\alpha \\ y=2\sin\alpha \end{cases}$$ (where α is the parameter). Establish a polar coordinate system with the origin of the coordinate system as the pole and the positive semi-axis of the x-axis as the polar axis. The polar equation of the curve C₂ is ρ=2sinθ.
(I) Write the polar equation of the curve C₁ and the rectangular equation of the curve C₂.
(II) Suppose point P is on C₁, point Q is on C₂, and ∠POQ=$$\frac {π}{3}$$, find the maximum area of △POQ.

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