
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 plane, there are two fixed points \( A \) and \( B \) on the \( x \)-axis, different from the origin \( O(0,0) \). A moving point \( C \) varies along the \( y \)-axis, and line \( l \) passes through \( O(0,0) \) and is perpendicular to line \( AC \). Find the trajectory of the intersection of line \( l \) with line \( BC \).

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