
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 \( C: \frac{x^{2}}{24}+\frac{y^{2}}{16}=1 \) and the line \( l: \frac{x}{12}+\frac{y}{8}=1 \), point \( P \) is a point on \( l \). The ray \( OP \) intersects the ellipse at point \( R \). Another point \( Q \) lies on \( OP \), satisfying \( |OQ| \cdot |OP| = |OR|^{2} \). As point \( P \) moves along \( l \), find the equation of the locus of point \( Q \), and describe what type of curve this locus represents.

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