<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Given in the Cartesian coordinate system $xOy$, a line $l$ passing through a fixed point $P$ with an inclination angle of $\alpha$ has the parametric equation: $$\begin{cases} x=t\cos\alpha \\ y=-2+t\sin\alpha \end{cases}$$ (where $t$ is the parameter). In the polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar coordinates of the center of the circle are $(3, \frac{\pi}{2})$, and the circle $C$ with a radius of 3 intersects the line $l$ at points $A$ and $B$. Then, $|PA|\cdot|PB|=$ \_\_\_\_\_. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
16
Given in the Cartesian coordinate system $xOy$, a line $l$ passing through a fixed point $P$ with an inclination angle of $\alpha$ has the parametric equation: $$\begin{cases} x=t\cos\alpha \\ y=-2+t\sin\alpha \end{cases}$$ (where $t$ is the parameter). In the polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar coordinates of the center of the circle are $(3, \frac{\pi}{2})$, and the circle $C$ with a radius of 3 intersects the line $l$ at points $A$ and $B$. Then, $|PA|\cdot|PB|=$ \_\_\_\_\_.
test