
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
Let the semi-focal distance of the hyperbola $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\ (a > 0, b > 0)$ be $c$, and $(a,0),(0,b)$ be two points on the line $l$. Given that the distance from the origin to the line $l$ is $\dfrac{\sqrt{3}}{4}c$, then the eccentricity of the hyperbola is ______.

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