
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, curve C₁ is defined by the parametric equations $$\begin{cases} x=\cos\theta \\ y=\sin\theta \end{cases}$$. After an affine transformation $$\begin{cases} x′= \sqrt {3}x \\ y′=2y\end{cases}$$, we obtain curve C₂. Using the coordinate origin O as the pole and the non-negative half of the x-axis as the polar axis, establish a polar coordinate system with the same unit length. Given line l: ρ(2cosθ - sinθ) = 8.

(I) Find the Cartesian equations of curve C₂ and line l.
(II) Let P be any point on curve C₂. Find the maximum distance from point P to line l and the coordinates of point P when this maximum distance is achieved.

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