
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 right focus of the hyperbola $\frac{x^{2}}{8}-y^2=1$ as the center, find the equation of the circle that is tangent to the hyperbola's asymptote.

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