
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 $C: \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1\ (a,b > 0)$, with its left and right foci being $F_1$ and $F_2$ respectively, a perpendicular line is drawn from $F_2$ to one of the asymptotes of the hyperbola $C$, and the foot of the perpendicular is $H$. If the midpoint $M$ of $F_2H$ lies on the hyperbola $C$, calculate the eccentricity of the hyperbola $C$.

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