
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
Let $C$ be an ellipse with equation $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1(a>b>0)$. The left vertex of the ellipse is $A$, and the right focus is $F$. A line $l$ passing through point $A$ with a slope of $30^{\circ}$ intersects the ellipse $C$ at another point $B$. If $BF\perp AF$, find the eccentricity of the ellipse $C$.

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