
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 $F_1(- \sqrt {10},0)$ and $F_2(\sqrt {10},0)$, $M$ is a point on this hyperbola and satisfies $\overrightarrow{MF_1} \cdot \overrightarrow{MF_2}=0$, and $|\overrightarrow{MF_1}| \cdot |\overrightarrow{MF_2}|=2$, determine the equation of this hyperbola.

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