
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 rectangular coordinate system, the parametric equations of curve $C$ are given by $\begin{cases} x=1+3\cos{\theta} \\ y=3+3\sin{\theta} \end{cases}$ ($\theta$ is the parameter), and the parametric equations of line $l$ are given by $\begin{cases} x=3+\frac{1}{2}t \\ y=3+\frac{\sqrt{3}}{2}t \end{cases}$ ($t$ is the parameter).

(1) Find the Cartesian 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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