
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 an elective course on Coordinate System and Parametric Equations, the following is given:  
The parametric equation of line $l$ is 
$$
\begin{cases}
x= \frac {1}{2}t \\
y= \frac { \sqrt {3}}{2}t+1
\end{cases}
$$  
(t is a parameter), and the parametric equation of curve $C$ is 
$$
\begin{cases}
x=2+\cos\theta \\
y=\sin\theta
\end{cases}
$$  
($\theta$ is a parameter).  
(1) Suppose in the polar coordinate system (which uses the same unit length as the Cartesian coordinate system $xOy$, with the origin $O$ as the pole and the positive x-axis as the polar axis), the polar coordinates of point P are $(4, \frac {\pi}{3})$. Determine the positional relationship between point P and line $l$.  
(2) Let point Q be a moving point on curve $C$. Find the difference between the maximum and minimum distances from point Q to line $l$.

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