
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 hyperbola $C$ be defined by $\dfrac{x^2}{a^2} - \dfrac{y^2}{16} = 1$ $(a > 0)$. The left and right foci of the hyperbola are denoted as $F_1$ and $F_2$, respectively. If a point $P$ on the hyperbola $C$ satisfies $|PF_1| - |PF_2| = 10$, then the equation of the asymptotes of this hyperbola is __________.

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