
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 a hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ ($$a > 0, b > 0$$) with two asymptotes perpendicular to each other, and the distance from one vertex to an asymptote is 2, find the distance from one focus of the hyperbola to an asymptote.

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