
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: $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \quad (a > 0, b > 0)$$ with its right focus at F(2, 0) and one of the directrices given by the equation $x = \frac{3}{2}$,
(1) find the standard equation and the asymptotes of hyperbola C;
(2) find the equation of the hyperbola that shares the asymptotes with hyperbola C and passes through the point P($\sqrt{3}$, 2).

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