
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 that point A lies on the circle C: x² + y² = 1, a line is drawn from point A perpendicular to the y-axis, intersecting the y-axis at point B. Point P satisfies the equation $\overrightarrow {BP}=2 \overrightarrow {BA}$.

1. Find the trajectory equation of point P.
2. Let Q be a point on the line l: x = 3, and O the origin of the coordinate system such that OP ⊥ OQ. Find the minimum value of the area of △POQ.

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