
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
Given the parametric equation of curve $C\_1$ as $\begin{cases} x=-1+t\cos \alpha \\ y=3+t\sin \alpha \end{cases}$ ($t$ is the parameter, $0\leqslant \alpha < \pi$), and the polar coordinate equation of curve $C\_2$ as $\rho =2\sqrt{2}\sin (\theta +\dfrac{\pi }{4})$, with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis:
(I) If the point $A$ with polar coordinates $(\sqrt{2},\dfrac{\pi }{4})$ lies on curve $C\_1$, find the coordinates of the intersection points of curves $C\_1$ and $C\_2$;
(II) If point $P$ has coordinates $(-1,3)$, and curves $C\_1$ and $C\_2$ intersect at points $B$ and $D$, find $|PB|\cdot|PD|$.

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