
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 $E: y^2 = 8x$ and the circle $M: (x - 2)^2 + y^2 = 4$, let point $N$ be a moving point on the parabola $E$, and let $O$ be the origin of the coordinates. The midpoint of the segment $ON$ is point $P$, whose trajectory is the curve $C$.

(Ⅰ) Find the equation of the curve $C$.

(Ⅱ) Let point $Q(x_0, y_0) (x_0 \geqslant 5)$ be a point on the curve $C$. Through point $Q$, draw two tangents to the circle $M$ that intersect the $x$-axis at points $A$ and $B$, respectively. Find the minimum value of the area of $\triangle QAB$.

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