
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
\( P P^{\prime} \) is any chord of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) 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}
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