
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, there is a line l₁: x = 2, and a curve C: {x = 2cosϕ, y = 2 + 2sinϕ} (where ϕ is a parameter). With O as the pole and the non-negative half-axis of the x-axis as the polar axis, establish a polar coordinate system. The polar coordinates of point M are $(3, \frac {π}{6})$.

1. Find the polar coordinate equations of the line l₁ and the curve C.
2. In the polar coordinate system, it is known that the ray ${l}_{2}：\;θ=α(0 < α < \frac{π}{2})$ intersects l₁ and C at points A and B respectively, and $|OA|\cdot |OB|=8 \sqrt {3}$. Find the area of △MOB.

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