
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 rectangular coordinate system on a plane, the parametric equations of curve $C$ are given by $\begin{cases} x = 2\cos θ \\ y = \sqrt{3}\sin θ \end{cases}$ ($θ$ is the parameter). A polar coordinate system is established with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The line $l$ passes through two points $A(\sqrt{2}, \frac{π}{4})$ and $B(3, \frac{π}{2})$ in the polar coordinate system.

(I) Write the general equation of curve $C$ and find the slope of line $l$.
(II) Suppose line $l$ intersects curve $C$ at points $P$ and $Q$. Compute $|BP| \cdot |BQ|$.

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