
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
A circle with equation $x^{2}+y^{2}=r^{2}$ passes through the right focus $F$ of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$. The circle intersects the asymptotes of the hyperbola at points $A$ and $B$ in the first and fourth quadrants, respectively. When the quadrilateral $OAFB$ is a rhombus, the eccentricity of the hyperbola is ____.

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