
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 C₁ are given by $$\left\{\begin{array}{l}x=1+2cosα \\ y= \sqrt{3}sinα\end{array}\right.$$ (where α is the parameter). By shortening the abscissa of all points on the curve C₁ to half of the original and the ordinate to $$\frac{ \sqrt{3}}{3}$$ of the original, we obtain the curve C₂. In the polar coordinate system with the coordinate origin O as the pole and the positive semi-axis of the x-axis as the polar axis, the polar equation of the straight line l is $$4ρsin(θ+ \frac {π}{3})+1=0$$.
(1) Find the polar equation of the curve C₂ and the rectangular equation of the straight line l;
(2) Let P be any point on the curve C₂, find the maximum value of the distance from point P to the straight line l.

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