
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
Some properties of a circle can be analogized to ellipses and hyperbolas. Given the proposition "A line $l$ intersects a circle $x^{2}+y^{2}=r^{2}$ at points $A$ and $B$, with the midpoint of $AB$ being $M$. If the slopes of line $AB$ and $OM$ ($O$ is the origin) both exist, then $k_{AB}k_{OM}=-1$," when analogized to an ellipse $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a > b > 0)$, the proposition becomes "A line $l$ intersects an ellipse $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a > b > 0)$ at points $A$ and $B$, with the midpoint of $AB$ being $M$. If the slopes of line $AB$ and $OM$ ($O$ is the origin) both exist, then $k_{AB}k_{OM}=$ _______"

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