
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
Let $F$ be a focus of the hyperbola $C$: $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1$. If there exists a point $P$ on $C$ such that the midpoint of the line segment $PF$ is exactly one endpoint of its imaginary axis, then the eccentricity of $C$ is ______.

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