
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
Let $O$ be the coordinate origin, and let $AB$ be a chord of a conic section that does not pass through point $O$ and is not perpendicular to the coordinate axes. Let $M$ be the midpoint of chord $AB$, and let $K_{AB}$ and $K_{OM}$ represent the slopes of lines $AB$ and $OM$, respectively. In the circle $x^{2}+y^{2}=r^{2}$, we have $K_{AB} \cdot K_{OM}=-1$. Analogously, in the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$, we can derive \_\_\_\_\_\_.

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