
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 $\frac{x^{2}}{2}-y^{2}=1$ with left and right foci $F_1$ and $F_2$, respectively, and a point $M(x_0, y_0)$ on the hyperbola that satisfies $\overrightarrow{MF_1} \cdot \overrightarrow{MF_2} \leq 0$, determine the range of values for $y_0$.

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