
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
Given the polar equation of curve \\(C_1\\) is \\(\rho = 4\cos \theta\\), and establishing a Cartesian coordinate system with the pole as the origin and the polar axis as the positive half-axis of \\(x\\), the parametric equation of curve \\(C_2\\) is \\(\left\{ \begin{array}{l} x = 3 - \frac{1}{2}t \\ y = \frac{\sqrt{3}t}{2} \end{array} \right.\\) (where \\(t\\) is the parameter), and point \\(A(3,0)\\).

\\((1)\\) Find the Cartesian equation of curve \\(C_1\\) and the general equation of curve \\(C_2\\);

\\((2)\\) Suppose curve \\(C_1\\) intersects with curve \\(C_2\\) at points \\(P\\) and \\(Q\\), calculate the value of \\(|AP| \cdot |AQ|\\).

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