
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). 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, $|PA|\cdot|PB|=$ \_\_\_\_\_.

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