
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 curve C₁: x+y=1 and the curve $$C_{2}:\begin{cases} x=2+2cos\phi \\ y=2sin\phi \end{cases}$$ (where φ is a parameter) are given. Establish a polar coordinate system with the coordinate origin as the pole and the non-negative semi-axis of the x-axis as the polar axis.

1. Write the polar equations for the curves C₁ and C₂.
2. In the polar coordinate system, the line l: θ=α (ρ>0) intersects with C₁ and C₂ at points A and B, respectively, where $$α∈(0, \frac{π}{2})$$. When $$\frac{|OB|}{|OA|}=4$$, find the value of α.

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