
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 cartesian coordinate plane $(xOy)$, point $A(0,-1)$ is given. Point $B$ lies on the line $y=-3$, and point $M$ satisfies $MB // OA$ and $||\overrightarrow{MA} \cdot \overrightarrow{AB}|| = ||\overrightarrow{MB}|| \cdot ||\overrightarrow{BA}||$. The locus of point $M$ is the curve $C$.

(I) Find the equation of curve $C$;

(II) Let $P$ be a moving point on curve $C$ and $l$ 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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