
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 C: y²=2px (p>0), a line passing through the point (4,0) intersects the parabola at points A(x₁, y₁) and B(x₂, y₂), with y₁y₂=-8.
(1) Find the value of p.
(2) Suppose a moving line l: y=kx+m is tangent to the parabola C at point P, and point Q is another point on line l. If a circle with PQ as its diameter always passes through a fixed point M on the x-axis, find the x-coordinate of point Q, x₀.

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