
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 points $B_{1}$ and $B_{2}$ are the two vertices on the imaginary axis of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 (a>0, b>0)$, a line passing through $B_{1}$ and perpendicular to the $y$-axis intersects the hyperbola at points $P$ and $Q$. If triangle $PQB_{2}$ is an equilateral triangle, then the eccentricity $e$ of the hyperbola is ______.

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