
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
Consider an ellipse \( C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0) \) with its left focus at point \( F \). A tangent to the ellipse at a point \( A \) intersects the \( y \)-axis at point \( Q \). Given that \( \angle Q F O = 45^{\circ} \) and \( \angle Q F A = 30^{\circ} \), determine the eccentricity \( e \) of the ellipse.

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