
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 that the distance from a moving point $M$ to the line $y = -2$ is one more than its distance to the point $F(0, 1)$,

(1) Find the trajectory equation of the moving point $M$;

(2) Suppose the curve formed by the moving point $M$ is $E$, and the line $l$ passing through the point $P(0, -1)$ intersects the curve $E$ at points $A$ and $B$. If the sum of the slopes of the lines $OA$ and $OB$ is $2$ (where $O$ is the origin), find the equation of the line $l$.

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