
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
The vertex of the parabola is at the origin, and its directrix passes through a focus of the hyperbola \\(\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 (a > 0, b > 0)\\) and is perpendicular to the real axis of the hyperbola. Given that one intersection point of the parabola and the hyperbola is \\(\left( \dfrac{3}{2}, \sqrt{6} \right)\\), find the equations of the parabola and the hyperbola.

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