
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, establish a polar coordinate system with the origin O as the pole and the positive semi-axis of the x-axis as the polar axis. The polar coordinate equations of the curves C₁ and C₂ are ρ=2 and ρ²+ $\sqrt {3}ρ$cosθ+ρsinθ=6, respectively.
(I) Find the rectangular coordinate equations of the curves C₁ and C₂;
(II) Suppose the common points of the curves C₁ and C₂ are A and B. Two mutually perpendicular lines are drawn through point O, intersecting line AB at points P and Q, respectively. Find the minimum value of the area of △OPQ.

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