
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
In the Cartesian coordinate plane $(xoy)$, the right branch of the hyperbola $\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1 (a > 0, b > 0)$ intersects with the parabola ${x}^{2}=2py (p > 0)$, which has a focus at point $F$, at two points $A$ and $B$. If $|AF| + |BF| = 4|OF|$, find the equations of the asymptotes of the hyperbola.

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