
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
Let F<sub>1</sub> and F<sub>2</sub> be the left and right foci of the ellipse C: $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ (where $a > b > 0$). If the sum of the distances from the point A $(0, \sqrt{3})$ on ellipse C to the foci F<sub>1</sub> and F<sub>2</sub> is 4,
1. Find the equation of the ellipse C.
2. Find the length of the minor axis and the focal distance of the ellipse C.

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