
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 $xOy$, the parametric equation of line $l$ is $$\begin{cases} x= \sqrt {3}- \frac { \sqrt {3}}{2}t \\ y= \frac {1}{2}t \end{cases}$$ (where $t$ is the parameter). In the polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, the polar equation of curve $C$ is $$\rho=2 \sqrt {3}\sin\theta$$.
(1) Write the Cartesian coordinate equation of curve $C$;
(2) Given that the intersection of line $l$ with the x-axis is point $P$, and its intersections with curve $C$ are points $A$ and $B$. If the midpoint of $AB$ is $D$, find the length of $|PD|$.

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