
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
Two rods each revolve around points \(A(a, 0)\) and \(B(-a, 0)\), and the product of their intercepts on the \(y\)-axis is \(b b_{1} = a^{2}\) (constant). Find the equation of the trajectory of the intersection point of the rods.

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