
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
Point P is a moving point on the curve C₁: (x-2)² + y² = 4. Establish a polar coordinate system with the coordinate origin O as the pole and the positive semi-axis of the x-axis as the polar axis. By rotating point P counterclockwise 90° around the pole O to obtain point Q, the trajectory of point Q is defined as curve C₂.
(I) Find the polar equations of curves C₁ and C₂;
(II) The ray θ = π/2 (ρ > 0) intersects curves C₁ and C₂ at points A and B, respectively. Given point M (2, 0), find the area of △MAB.

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