
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 parametric equations of line $l$ are given by $\begin{cases} x = -1 + t\cos\alpha \\ y = \frac{1}{2} + t\sin\alpha \end{cases}$ ($t$ is a parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C$ is given by $\rho^2 = \frac{4}{4\sin^2\theta + \cos^2\theta}$.

(I) Write the rectangular coordinate equation of curve $C$;

(II) If the rectangular coordinates of point $P$ are $\left(-1, \frac{1}{2}\right)$, and line $l$ intersects curve $C$ at two distinct points $A$ and $B$, find the range of values for $|PA| \cdot |PB|$.

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