
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, a pole coordinate system is established 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 curve C₁ is ρcosθ=4.
1. M is a moving point on the curve C₁, and point P is on the line segment OM, satisfying |OM|•|OP|=16. Find the rectangular coordinate equation of the trajectory C₂ of point P.
2. If point A has polar coordinates $(2, \frac {π}{3})$, and point $B(2 \sqrt {3} ,θ)$ is on the curve C₂, find the area of △ABO.

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