
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
It is known that a hyperbola has two foci F<sub>1</sub> (-$$\sqrt{10}$$, 0) and F<sub>2</sub> ($$\sqrt{10}$$, 0). Point P lies on the hyperbola, and $$\overrightarrow{PF_1} \cdot \overrightarrow{PF_2} = 0$$, |$$\overrightarrow{PF_1}$$| |$$\overrightarrow{PF_2}$$| = 2. Find the equation of this hyperbola.

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