
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 hyperbola H_{1} is given by $\frac{x^{2}}{20} - \frac{y^{2}}{5} = 1$, which shares the same asymptotes with the hyperbola H_{2}. The point $(2\sqrt{15}, \sqrt{5})$ is on H_{1}. Determine the distance from the focus of H_{1} to the asymptote.

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