
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 an ellipse with the equation
$$
\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \quad (a > b > 0)
$$
where points \(A\) and \(B\) are the endpoints of the major axis, and point \(P\) is another point on the ellipse (different from \(A\) and \(B\)). Lines \(l_1 \perp PA\) and \(l_2 \perp PB\) are drawn through points \(A\) and \(B\) respectively, and intersect at point \(M\). Find the equation of the locus of point \(M\) as point \(P\) moves along the ellipse.

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