
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 \(\frac{x^{2}}{20}+\frac{y^{2}}{16}=1\) which intersects the \(x\)-axis at points \(A\) and \(B\), a tangent line \(l\) is drawn from a point \(M\) on the ellipse (where \(M\) is not coincident with \(A\) or \(B\)). Perpendicular lines are drawn from points \(A\) and \(B\) to the \(x\)-axis, intersecting the tangent line \(l\) at points \(C\) and \(D\) respectively. The lines \(CB\) and \(AD\) intersect at point \(Q\). Point \(P\) is the symmetric point of \(Q\) with respect to \(M\). Find the equation of the locus of point \(P\).

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