
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 $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 \left(a > 0, b > 0\right)$ with its right focus at $F(c,0)$ and the line $x= \dfrac{a^2}{c}$ intersects with one of the asymptotes at point $A$, find the equation of the directrix of the parabola ${y}^{2}= \dfrac{4a}{b}x$.

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