
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 the center of hyperbola C is the origin, and its right focus is F($$\sqrt{3}$$, 0),
(1) When the eccentricity e of the hyperbola C is $$\sqrt{3}$$, find the standard equation of this hyperbola C.
(2) If the equation of one asymptote of hyperbola C is X + $$\sqrt{2}$$Y = 0, find the standard equation of this hyperbola C.

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