
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 Cartesian coordinate system \(xOy\), there is a point \(P(0, \sqrt{3})\) and a line \(l\) with the parametric equations \(\begin{cases} x = \dfrac{1}{2}t \\ y = \sqrt{3} + \dfrac{\sqrt{3}}{2}t \end{cases}\) (where \(t\) is the parameter). Using the origin as the pole and the non-negative half-axis of \(x\) to establish a polar coordinate system, the polar equation of curve \(C\) is \(\rho^2 = \dfrac{4}{1+\cos^2\theta}\).
(1) Find the general equation of line \(l\) and the Cartesian equation of curve \(C\).
(2) Suppose line \(l\) intersects curve \(C\) at points \(A\) and \(B\). Calculate the value of \(\dfrac{1}{|PA|} + \dfrac{1}{|PB|}\).

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