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

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