
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
In a Cartesian coordinate system, there are two fixed points $A$ and $B$ on the $x$-axis different from the origin $O(0,0)$. A moving point $C$ varies on the $y$-axis, and the line $l$ passes through $O(0,0)$ and is perpendicular to the line $AC$. Find the locus of the intersection point of the lines $l$ and $BC$.

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