
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 a polar coordinate system with the origin O as the pole and the positive x-axis as the polar axis, the polar coordinate of point P is $(\sqrt{2}, \frac{\pi}{4})$. A line l passes through point P with an angle of inclination $\frac{2\pi}{3}$. The curve corresponding to the equation $\frac{x^2}{36} + \frac{y^2}{16} = 1$ undergoes the scaling transformation $\begin{cases} x' = \frac{1}{3}x \\ y' = \frac{1}{2}y \end{cases}$ resulting in curve C.
(I) Find the parametric equation of line l and the equation of curve C in the Cartesian coordinate system.
(II) Line l intersects curve C at two points A and B. Find the value of $|PA| \cdot |PB|$.

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