
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
Given the parametric equations of curve C₁ as $$\begin{cases} x=3+2cos\alpha \\ y=1+2sin\alpha \end{cases}$$ (where α is the parameter), P is any point on curve C₁. Draw a perpendicular line from P to the y-axis, with Q as the foot of the perpendicular. The locus of the midpoint of line segment PQ is curve C₂.
(I) Find the Cartesian equation of curve C₂.
(II) Establish a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis. If line l: $sinθ - cosθ = \frac{1}{ρ}$ intersects curve C₂ at points M and N, find |MN|.

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