
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 $$C: \frac {x^{2}}{4}- \frac {y^{2}}{3}=1$$, its right vertex is P.  
(1) Find the standard equation of the circle with center P that is tangent to both asymptotes of the hyperbola C;  
(2) Let line l pass through point P, with the normal vector $$\overrightarrow {n}$$ = (1, -1). If there are exactly three points P<sub>1</sub>, P<sub>2</sub>, P<sub>3</sub> on the hyperbola C that are all at distance d from line l, find the value of d.

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