
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 two foci of a hyperbola are $F\_1(0, \sqrt{10})$ and $F\_2(0, -\sqrt{10})$, and $M$ is a point on this hyperbola such that $\overrightarrow{MF\_1} \cdot \overrightarrow{MF\_2} = 0$ and $|\overrightarrow{MF\_1}| \cdot |\overrightarrow{MF\_2}| = 2$, find the standard equation of the hyperbola.

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