
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 the hyperbola $C$: $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 (a > 0, b > 0)$, where the left and right foci are $F_1$ and $F_2$ respectively, $P$ is a point on the hyperbola $C$, and $Q$ is a point on the asymptote of hyperbola $C$. Both $P$ and $Q$ are located in the first quadrant, and $\overrightarrow{QP} = \overrightarrow{PF_2}$, $\overrightarrow{QF_1} \cdot \overrightarrow{QF_2} = 0$. Then, the eccentricity of the hyperbola $C$ is \_\_\_\_\_\_.

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