
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 a Cartesian coordinate system, it is known that line $l$ passes through point $P(-1, 2)$ and has an inclination angle $\alpha = \frac{\pi}{6}$. A polar coordinate system is established with the origin as the pole and the positive half of the x-axis as the polar axis. The polar equation of curve $C$ is $\rho = 3$.

(Ⅰ) Write the parametric equation of line $l$ and the Cartesian equation of curve $C$.
(Ⅱ) If line $l$ intersects curve $C$ at points $M$ and $N$, find the value of $|PM| \cdot |PN|$.

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