
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 parabola E: y²=8x, circle M: (x-2)²+y²=4, point N is a moving point on parabola E, O is the origin, and the midpoint of segment ON is P. The trajectory of point P forms curve C.
(1) Find the equation of curve C;
(2) Point Q(x₀, y₀) (x₀≥5) is a point on curve C. Two tangent lines are drawn from point Q to circle M, intersecting the x-axis at points A and B. Find the minimum value of the area of △QAB.

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