
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 $F$ is the focus of the parabola $C: y^{2}=2px\left(p \gt 0\right)$, and the directrix of the parabola $C$ intersects the two asymptotes of the hyperbola $Γ: \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1(a＞0,b＞0)$ at points $A$ and $B$. If triangle $ABF$ is an equilateral triangle, calculate the eccentricity $e$ of $Γ$.

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