
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, the origin coincides with the pole of the polar coordinate system, and the positive $x$-axis is the polar axis. The line $l$ passes through the point $P(-1,1)$, and its slope angle is $\alpha=\frac{5\pi}{6}$. The polar equation of the curve $C$ is $\rho=4\sin\theta$.
(I) Find the parametric equation of line $l$ and the Cartesian equation of curve $C$;
(II) Suppose line $l$ intersects curve $C$ at points $A$ and $B$. Find the value of $\overrightarrow{PA}\cdot\overrightarrow{PB}$.

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