
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 and foci on the y-axis, a point P on the ellipse has a sum of distances to the two foci (F1 and F2) of 4, and an eccentricity of √3/2.
(1) Find the equation of the ellipse (C);
(2) If the line y = kx + 1 intersects the curve (C) at points A and B, find the range of values for the area of triangle AOB.

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