
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 the foci of a hyperbola $C$ are $F_{1}(0,2)$ and $F_{2}(0,-2)$, and the length of the real axis is $2$, the eccentricity of the hyperbola $C$ is ____; if point $Q$ lies on the asymptote of the hyperbola $C$ and $F_{1}Q\perp F_{2}Q$, then the area of $\triangle QF_{1}F_{2}$ is ____.

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