
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 $l$ as $\begin{cases} x=1- \frac { \sqrt {3}}{2}t \\ y= \sqrt {3}+ \frac {1}{2}t\end{cases}$ (where $t$ is the parameter), with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis to establish the polar coordinate system, the polar equation of circle $C$ is $\rho=4\cos (\theta- \frac {\pi}{3})$  
(Ⅰ) Find the Cartesian coordinate equation of curve $C$;  
(Ⅱ) If point $P(x,y)$ is a moving point on line $l$ that is inside circle $C$ (including the endpoints), find the maximum and minimum values of $\sqrt {3}x+y$.

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