
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 C with its center at the origin and its right focus at (2, 0), with a real axis length of 2$\sqrt{3}$.
(1) Find the standard equation of hyperbola C;
(2) Find the distance from the right focus of hyperbola C mentioned in (1) to the asymptote.

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