
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 the hyperbola $$C:\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,$$, and the circle $$E:{{(x-2)}^{2}}+{{y}^{2}}=1$$ whose center is the right focus of the hyperbola $$C$$. If the circle $$E$$ is tangent to the asymptote of the hyperbola $$C$$, then the equation of the hyperbola $$C$$ is _______.

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