
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 Cartesian coordinate system xOy, the parametric equations of the curve C₁ are given by: $$\begin{cases} x=2+2\cos\alpha \\ y=2\sin\alpha \end{cases}$$ (where α is the parameter). Establish a polar coordinate system with the origin O of the Cartesian coordinate system as the pole and the non-negative semi-axis of the x-axis as the polar axis. The polar coordinate equation of the line C₂ is given by: ρcosθ + ρsinθ = 2.
(1) Determine the ordinary equation of the curve C₁ and the rectangular coordinate equation of the line C₂.
(2) If the intersection points of C₁ and C₂ are denoted by A and B, calculate the area of ∆AOB.

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