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

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