
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 ellipse C₁: $\frac{x^2}{4}$ + $y^2$ = 1, with left and right vertices A and B, respectively. Point P is a moving point on the ellipse C₁, distinct from A and B. Let the slopes of lines PA and PB be k₁ and k₂, respectively. If the moving point Q has slopes k₃ and k₄ with respect to lines connecting A and B, and k₃k₄ = λk₁k₂ (λ ≠ 0), then the trajectory of moving point Q is denoted as curve C₂.

(I) Find the equation of curve C₂ when λ = 4.
(II) Given point M (1, $\frac{1}{2}$), lines AM and BM intersect curve C₂ at points E and F, respectively. Let S₁ be the area of △AMF and S₂ be the area of △BME. If λ ∈ [1, 3], find the range of $\frac{S_1}{S_2}$.

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