
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
This question is worth 10 points. Elective 2-1: Conic Sections and Equations. In the Cartesian coordinate system xOy, it is known that point A is at (0, -1), point B is on the line y = -3, and point M satisfies $\overrightarrow{MA} \cdot \overrightarrow{MB} = \overrightarrow{MA} \cdot \overrightarrow{MM}$. The trajectory of point M is curve C.
(1) Find the equation of curve C;
(2) Let P be a moving point on curve C, and l be the tangent line to C at point P. Find the minimum distance from point O to line l.

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