
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 \(2 y^{2}-2 x^{2}=1\), find the range of values for \(\overrightarrow{F A} \cdot \overrightarrow{F B}\) where the line \(l\) through the point \(F(0,1)\) intersects the hyperbola at points \(A\) and \(B\).

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