
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 $M(x\_0, y\_0)$ is a point on the hyperbola $C$: $\frac{x^2}{2} - y^2 = 1$, and $(F\_1, F\_2)$ are two foci of $C$. If $\overset{\to}{\;MF\_1} \cdot \overset{\to}{\;MF\_2} < 0$, then the range of values for $y\_0$ is $\_\_\_\_\_\_\_\_$.

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