
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 $C: \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ ($a > 0, b > 0$), the right focus of $C$ is $F$, and the point $M$ in the first quadrant is on the asymptote of hyperbola $C$, with $|OM| = a$. If the slope of line $MF$ is $-\dfrac{b}{a}$, calculate the eccentricity of hyperbola $C$.

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