
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 parametric equation of line $l$: 
$$
\begin{cases}
  x=-1- \frac { \sqrt {3}}{2}t \\
  y= \sqrt {3}+ \frac {1}{2}t
\end{cases}
$$
(where $t$ is the parameter), with the coordinate origin as the pole and the positive x-axis as the polar axis, the polar equation of circle $C$ is $\rho=4\sin(\theta- \frac {\pi}{6})$.
1. Find the Cartesian coordinate equation of circle $C$.
2. If $P(x,y)$ is the intersection point of line $l$ and the circular area $\rho \leq 4\sin(\theta- \frac {\pi}{6})$, find the range of $\sqrt {3}x+y$.

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