
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 circle O: x²+y²=1, P is any point on circle O, and a vertical line is drawn from point P to the x-axis, with the foot of the perpendicular being P". Point Q is on line segment PP", and $\overrightarrow {PQ}$=2$\overrightarrow {QP}$′. Determine the equation of the trajectory of point Q.

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