
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 a circle C: x²+y²=1, let P be any point on the circle. Draw a line PQ perpendicular to the y-axis, with Q as the foot of the perpendicular, and $\overrightarrow{OM} = \sqrt{3}\overrightarrow{QP}$.

(I) Find the equation of the trajectory E of the moving point M.
(II) Let l be a tangent line to the circle C, intersecting the curve E at points A and B. Find the maximum value of |AB|.

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