
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
Consider the hyperbola $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1$$. The vertical line drawn from the right vertex of the hyperbola intersects one of its asymptotes at point A. Additionally, a circle with a radius of 4 and centered at the right focus of the hyperbola passes through both point A and the origin O. Determine the equation of the hyperbola C.

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