
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 equation of the curve C₁ is $$\begin{cases} \overset{x=cost}{y=1+sint}\end{cases}$$ (t is the parameter). In the polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the x-axis as the polar axis, the circle C₂: ρ=4cosθ has its center at C₂.
(I) Explain what kind of curve C₁ is and convert the equation of C₁ into polar coordinates;
(II) The line C₃ passing through the origin and parallel to the line $$\begin{cases} \overset{x=2+tcos\alpha }{y=3+tsin\alpha }\end{cases}$$ (t is the parameter, 0≤α<π) intersects with C₂ at points M and N. The area of △C₂MN is 2. Find the value of α.

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