
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 plane Cartesian coordinate system, the line \(l\) passes through the origin, with an inclination angle \(\theta =\dfrac{\pi}{3}\). Establishing a polar coordinate system with the origin as the pole and the positive \(x\)-axis as the initial line, the polar equation of curve \(C\) is given by \(\rho^2\cos^2\theta + \rho^2\sin^2\theta - 2\rho\sin\theta - 3 = 0\).

1. Find the parametric equation of the line \(l\).
2. If the line \(l\) intersects the curve \(C\) at points \(A\) and \(B\), find the length of \(|AB|\).

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