
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 on a plane, a polar coordinate system is established with the origin as the pole and the non-negative semi-axis of the x-axis as the polar axis. The polar coordinate equation of the curve C is given as ρ² = 2ρcosθ - 4ρsinθ + 4, and the polar coordinate equation of the line l₁ is given as ρ(cosθ - sinθ) = 3.
(I) Write the rectangular coordinate equations for curve C and line l₁.
(II) Suppose line l₂ passes through point P(-1, 0) and intersects curve C at two distinct points A and B. The midpoint of AB is M, and the intersection of l₁ and l₂ is N. Find |PM| • |PN|.

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