
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 an ellipse $C: \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1\left(a \gt b \gt 0\right)$ and a parabola $E: y^{2}=2px\left(p \gt 0\right)$ with a common focus $F$, where the ellipse $C$ and the parabola $E$ intersect at points $A$ and $B$, and $A$, $B$, $F$ are collinear, find the eccentricity of the ellipse $C$.

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