
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, 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 coordinate equation of the curve C1 is ρ=4cosθ, and the polar coordinate equation of the curve C2 is ρ= $\sqrt {3}$sinθ. The polar coordinate equation of the straight line l that does not coincide with the coordinate axis is θ=θ₀ (ρ∈R). Let l intersect with the curves C1 and C2 at points A and B respectively, which are distinct from the pole.
(I) When θ₀ = $\frac {3π}{4}$, find the distance |AB|.
(II) Find the rectangular coordinate equation of the trajectory of the midpoint of AB.

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