
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: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (where $a > b > 0$) that passes through the point $(-1, \frac{3}{2})$ and has an eccentricity of $\frac{1}{2}$, a line l passes through the point $P(1, 0)$ and intersects the ellipse C at points M and N.

(I) Find the standard equation of the ellipse C.
(II) Knowing the origin is denoted as O and $\overrightarrow{PO} = \overrightarrow{OR}$, find the maximum area of $\triangle MNR$ and the equation of the line l at that time.

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