
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 that one asymptote of the hyperbola C is $$\sqrt {3}x+y=0$$, and it passes through point P$$( \sqrt {2}， \sqrt {3})$$.
(1) Find the standard equation of the hyperbola;
(2) If line l: y=kx+2 intersects with hyperbola C at exactly 1 point, find the value of the real number k.

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