
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 system $(xOy)$, point $A(0,-1)$ and point $B$ are on the line $y=-3$. Point $M$ satisfies $\overrightarrow{MB} \parallel \overrightarrow{OA}$ and $\overrightarrow{MA} \cdot \overrightarrow{AB} = \overrightarrow{MB} \cdot \overrightarrow{BA}$. Find the trajectory equation of point $M$.

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