
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
The equations of the asymptotes of a hyperbola are \( y= \pm 2(x-1) \), and one of its foci is at \( (1+2\sqrt{5}, 0) \). Find the equation of the hyperbola.

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