
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
In the Cartesian coordinate system $xOy$, the ellipse $C: \frac{x^2}{2} + \frac{y^2}{3} = 1$ has a focus on the positive y-axis denoted as $F$. A line $l$ passing through $F$ with a slope angle of $\frac{3\pi}{4}$ intersects $C$ at points $M$ and $N$. The quadrilateral $OMPN$ is a parallelogram.
(1) Determine the positional relationship between point $P$ and the ellipse;
(2) Calculate the area of the parallelogram $OMPN$.

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