
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, with the origin as the pole and the positive half-axis of _x_ as the polar axis, a polar coordinate system is established. The polar equation of curve \\(C\\) is \\(\rho-2\cos\theta-6\sin\theta+\frac{1}{\rho}=0\\), and the parametric equation of line _l_ is \\(\begin{cases}x=3+\frac{1}{2}t \\ y=3+\frac{\sqrt{3}}{2}t\end{cases}\\) (where _t_ is the parameter).

\\((1)\\) Find the general equation of curve \\(C\\).

\\((2)\\) If line _l_ intersects curve \\(C\\) at points \\(A\\) and \\(B\\), and the coordinates of point \\(P\\) are \\((3,3)\\), find the value of \\(|PA|+|PB|\\).

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