
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 curve C with the polar coordinate equation ρ²(1 + 3sin²θ) = 4, where O is the origin and the positive semi-axis of the x-axis is the polar axis.
(I) Find the parametric equation of curve C;
(II) The curve intersects the positive semi-axis of the x-axis and the positive semi-axis of the y-axis at points A and B, respectively. A point P is taken on the curve C in the first quadrant. Find the maximum value of the area of the quadrilateral OAPB.

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