
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
The left and right foci of the hyperbola $C: \frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$ ($a > 0$, $b > 0$) are denoted as F<sub>1</sub> and F<sub>2</sub>, respectively. Let A be a point on the right branch of the hyperbola, and the line segment AF<sub>1</sub> intersects the left branch at point B, with $\overrightarrow {F_{1}A} = 3 \overrightarrow {F_{1}B}$ and $| \overrightarrow {OF_{1}}|= | \overrightarrow {OA}|$ (O is the origin of the coordinates). Find the equation of the asymptotes of the hyperbola C.

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