
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 line $l$: $ \begin{cases} x=1+ \frac {1}{2}t \\ y= \sqrt {3}+ \frac{ \sqrt {3}}{2}t \end{cases} (t\text{ is a parameter})$, with the origin as the pole and the non-negative semi-axis of the $x$-axis as the polar axis, establish a polar coordinate system. The polar equation of the curve $C$ is $ρ^{2}-2 \sqrt {3}ρ\sin θ=a (a > -3)$.
(I) Convert the polar coordinate equation of the curve $C$ to rectangular coordinates;
(II) If the curve $C$ intersects the line $l$ at a unique point, find the value of the real number $a$.

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