
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
Let line $l$ pass through point $P(-3,3)$, and its angle of inclination is $\frac{5\pi}{6}$.

$(1)$ Write the standard parametric equation of line $l$;

$(2)$ Suppose this line intersects curve $C: \begin{cases}x=2\cos \theta \\ y=4\sin \theta\end{cases}$ (where $\theta$ is the parameter) at points $A$ and $B$, find the value of $|PA|\cdot|PB|$.

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