
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 Oxy, curve C₁ is defined by the parametric equations $$\begin{cases} x=4+4\cos\alpha \\ y=4\sin\alpha \end{cases}$$ (where α is the parameter), and curve C₂ has the polar coordinate equation ρ² - 4ρcosθ - 4 = 0 with O as the pole and the positive semi-axis of the x-axis as the polar axis.
(I) Find the Cartesian equation for curve C₁ and the polar coordinate equation for curve C₂.
(II) Point P is an intersection of curves C₁ and C₂. A tangent line is drawn to curve C₁ at point P and intersects curve C₂ at another point Q. Find the length |PQ|.

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