
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 a straight line \( y = kx + b (b \neq 0) \) and a quadratic curve 
\[ Ax^{2} + 2Bxy + Cy^{2} + 2Dx + 2Ey + F = 0 \]
that intersect at points \( M \) and \( N \), find the necessary and sufficient condition for the straight lines \( OM \) and \( ON \) to be perpendicular.

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