
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, points A(-1, 0) and B(2, 0) are given. A moving point M satisfies the condition $|MA|/|MB| = 1/2$. Denote the trajectory of the moving point M as C.
(I) Find the equation of curve C.
(II) If a fixed point P(0, a) (a > 0) is given and the maximum value of the line segment |MP| is $2 + 2\sqrt{2}$, find the equation of the tangent line l passing through point P and curve C.

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