
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 that the center of the ellipse $(E)$ is at the origin of the coordinate, the eccentricity is $\frac{1}{2}$, the right focus of $(E)$ coincides with the focus of the parabola $(C:y^{2}=8x)$, and $A,B$ are the two intersection points of the latus rectum of $(C)$ and $(E)$. Find the length of $|AB|$.

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