
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
In the Cartesian coordinate plane $(xOy)$, a given ellipse $(C)$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ intersects with line $(l)$: $y=kx+m$, which does not pass through the coordinate origin $O$, at points $A$ and $B$. The midpoint of segment $AB$ is $M$. If the product of the slopes of $AB$ and $OM$ is $(-\frac{3}{4})$, find the eccentricity of ellipse $(C)$.

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