
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 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). With the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar coordinates of the center of the circle are $(3, \frac{\pi}{2})$, and the radius of the circle $C$ is $3$. The circle $C$ intersects the line $l$ at points $A$ and $B$. Then, $|PA|\cdot|PB|=$ \_\_\_\_\_\_.

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