
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 equation of curve C₁ is given by $$\begin{cases} x=\cos\alpha \\ y=\sin\alpha \end{cases}$$ (where α is a 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 coordinate equation of curve C₂ is ρ=2cosθ.
(I) Find the rectangular coordinates of the intersection points of C₁ and C₂.
(II) Suppose point A has polar coordinates $$(4, \frac{\pi}{3})$$, and point B is on curve C₂. Find the maximum area of triangle AOB.

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