
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 points $E(0,1)$ and $K(0,-1)$, $P$ is a moving point on the coordinate plane that satisfies $||\overrightarrow{PE}|| \cdot ||\overrightarrow{KE}|| = \overrightarrow{PK} \cdot \overrightarrow{EK}$. Let the trajectory of point $P$ be denoted by $C$.

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

(II) Draw two tangent lines, $MA$ and $MB$, from a point $M$ on the line $y=x-2$ to curve $C$. The tangent points are denoted as $A$ and $B$, respectively. If $MA \perp MB$, find the equation of line $AB$.

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