
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
Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system, the parametric equation of line \\(l\\) is \\(\begin{cases}x=t+1 \\\\ y= \sqrt{3}t+1\end{cases} \\) (where \\(t\\) is the parameter). With the origin as the pole and the positive half-axis of \\(x\\) as the polar axis, the polar equation of curve \\(C\\) is \\(\rho= \dfrac{2\cos \theta}{1-\cos^2\theta} \\).

\\((1)\\) Write the polar equation of line \\(l\\) and the Cartesian equation of curve \\(C\\);

\\((2)\\) It is known that the line \\(l'\\) parallel to line \\(l\\) passes through point \\(M(2,0)\\) and intersects curve \\(C\\) at points \\(A\\) and \\(B\\). Find \\(|AB|\\).

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