
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 left and right foci as $F_1(-c,0)$ and $F_2(c,0)$ respectively, and the circle with diameter $F_1F_2$ intersects the hyperbola at point $P$ in the second quadrant. If the line $PF_2$ is tangent to the circle $E$: $(x-\dfrac{c}{2})^2 + y^2 = \dfrac{b^2}{16}$, find the equation of the asymptote of the hyperbola.

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