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

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