
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
\(PP^{\prime}\) is any chord of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) that is parallel to the \(y\)-axis. \(A\) and \(A^{\prime}\) are the two vertices on the \(x\)-axis. The lines \(A^{\prime} P\) and \(A P^{\prime}\) intersect at \(Q\). Find the locus of \(Q\).

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