
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 $F\_1$ and $F\_2$ are the left and right foci of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 (a > 0, b > 0)$, there exists a point $P$ on the hyperbola such that $\angle F\_1 P F\_2 = 60^{\circ}$ and $|OP| = 3b$ (where $O$ is the coordinate origin). Determine the eccentricity of this hyperbola.

A) $\frac{4}{3}$
B) $\frac{2 \sqrt{3}}{3}$
C) $\frac{7}{6}$
D) $\frac{\sqrt{42}}{6}$

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