
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 an ellipse C with its center at the origin that passes through point A (2, 3) and has a right focus at point F (2, 0).
(1) Find the equation and eccentricity e of ellipse C;
(2) If a line l parallel to OA intersects the ellipse at some points, find the range of the y-intercept of line l on the y-axis.

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