
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 rectangular coordinate system $xOy$, the parametric equations of the curve $C_1$ are given by $$\begin{cases} x=1+2\cos\alpha \\ y= \sqrt {3}\sin\alpha\end{cases}$$ (where $\alpha$ is the parameter). By reducing the abscissa of all points on the curve $C_1$ to $\frac {1}{2}$ of the original and the ordinate to $\frac { \sqrt {3}}{3}$ of the original, we obtain the curve $C_2$. In the polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of the line $l$ is $4\rho\sin({\theta+ \frac {π}{3}})+1=0$.
   (1) Find the polar equation of the curve $C_2$ and the rectangular equation of the line $l$.
   (2) Let point $P$ be any point on the curve $C_3$: $\frac {y^{2}}{3}$+$x^2$=$1$, find the maximum value of the distance from point $P$ to line $l$.

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