
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 polar coordinate system, the polar equation of curve $C$ is given by $ρ=4 \sqrt {2}\sin (θ+ \dfrac {π}{4})$. Establish a Cartesian coordinate system with point $O$ as the origin and the non-negative half of the polar axis as the $x$-axis. The parametric equations of line $l$ are given by $ \begin{cases} x=-2+ \dfrac {1}{2}t \\ y=-3+ \dfrac { \sqrt {3}}{2}t\\ \end{cases}(t \text{ is the parameter}). $

(I) Write the Cartesian equations of line $l$ and curve $C$;

(II) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, and point $P(-2,-3)$ is defined. Find the value of $|PA|⋅|PB|$.

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