
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 are $$\begin{cases} x=1+2\cos\theta, \\ y= \sqrt {3}+2\sin\theta\end{cases}$$ (where θ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the x-axis as the polar axis. The polar coordinate equation of the straight line l₁ is $$θ=α(0＜α＜ \frac {π}{2})$$. Rotate the straight line l₁ counterclockwise around the pole O by $$\frac {π}{3}$$ units to obtain the straight line l₂.

1. Find the polar coordinate equations of C and l₂.
2. Suppose the straight line l₁ and the curve C intersect at O, A two points, and the straight line l₂ and the curve C intersect at O, B two points. Find the maximum value of |OA|+|OB|.

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