
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 $(xOy)$, the slope angle of line $l$ passing through point $P(1,-2)$ is $45^{\circ}$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semiaxis of the $x$-axis as the polar axis. The polar equation of curve $C$ is $\rho \sin^2 \theta = 2 \cos \theta$. The intersection points of line $l$ and curve $C$ are points $A$ and $B$.
(I) Find the parametric equation of line $l$;
(II) Calculate the value of $|PA| \cdot |PB|$.

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