
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
Given points A(x₀, 0) and B(0, y₀) moving on the x-axis and y-axis respectively, with |AB|=1. If the moving point P(x, y) satisfies the equation $\overrightarrow{OP} = 2\overrightarrow{OA} + \sqrt{3}\overrightarrow{OB}$,

1. Find the standard equation of the trajectory curve C corresponding to the moving point P.
2. A line l₁ with a y-intercept of 2 intersects curve C at points P and Q. If a circle with PQ as the diameter passes through the origin, find the equation of the line.

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