
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 $C: \frac{x^{2}}{24}+\frac{y^{2}}{16}=1$, the line $l: \frac{x}{12}+\frac{y}{8}=1$, point $P$ is on $l$, the ray $OP$ intersects the ellipse at point $R$, and point $Q$ lies on $OP$ such that $|O Q| \cdot |O P|=|O R|^{2}$. When point $P$ moves along $l$, find the equation of the locus of point $Q$; also describe what type of curve the locus is.

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