
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
Consider the hyperbola $C: \frac{x^{2}}{a^{2}}- \frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$. Let $F_{1}$, $F_{2}$ be its left and right foci, and $A$ be a point on the right branch. If $AF_{1}$ intersects the left branch of the hyperbola at point $B$, and $\overrightarrow{F_{1}A} = 3\overrightarrow{F_{1}B}$, $|\overrightarrow{OF_{1}}| = |\overrightarrow{OA}|$ ($O$ is the coordinate origin), then the equations of the asymptotes of hyperbola $C$ are \_\_\_\_\_\_.

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