
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
Find the equations of the \( n \) lines that pass through the origin and are perpendicular to the \( n \) lines represented by \( a_{0} x^{n} + a_{1} x^{n-1} y + a_{2} x^{n-2} y^{2} + \cdots + a_{n} y^{n} = 0 \).

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