
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 hyperbola $C$: $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 \ (a > 0, b > 0)$ has its left and right foci at $F_1(-c,0)$ and $F_2(c,0)$, respectively. Points $M$ and $N$ are on the hyperbola $C$, and $MN \perp F_1F_2$, with $|F_1F_2| = 4|MN|$. The line segment $F_1N$ intersects the hyperbola $C$ at point $Q$, and $|F_1Q| = |QN|$. The eccentricity of the hyperbola $C$ is __________.

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