
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 the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, where $A$ and $B$ are the right and upper vertices, respectively, and $F$ is the left focus. A circle centered at the origin is tangent to the line $BF$ and intersects the positive semi-axis of the $y$-axis at point $C$. The line passing through point $C$ intersects the ellipse at points $M$ and $N$. If the quadrilateral $FAMN$ is a parallelogram, find the eccentricity of the ellipse.

A) $\frac{3}{5}$
B) $\frac{1}{2}$
C) $\frac{2}{3}$
D) $\frac{3}{4}$

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