
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 hyperbola $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ with its right focus at $F(2,0)$, let $A$ and $B$ be two points on the hyperbola symmetric about the origin. The midpoint of $AF$ is $M$, and the midpoint of $BF$ is $N$. If the origin $O$ lies on the circle with diameter $MN$, and the slope of line $AB$ is $\dfrac{3 \sqrt{7}}{7}$, calculate the eccentricity of the hyperbola.

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