
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 the x-axis 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 $\begin{cases} x=3+ \frac{1}{2}t \\ y=3+ \frac{\sqrt{3}}{2}t \end{cases}$ (t is the parameter).
(1) Find the standard 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}
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