
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 that F is the right focus of the hyperbola C: $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ ($a > 0, b > 0$), $l_1$ and $l_2$ are the two asymptotes of C. Point A is on $l_1$ and $FA \perp l_1$, point B is on $l_2$ and $FB \parallel l_1$. If $|FA| = \dfrac{4}{5}|FB|$, determine the eccentricity of the hyperbola C.

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