
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
Let $A$, $B$ be two points on the curve $C$: $x^{2} = y$, such that the product of their x-coordinates is $-1$.  
(i) Determine whether the line $AB$ always passes through a fixed point, and explain your reasoning;  
(ii) Suppose that the tangents to curve $C$ at points $A$ and $B$ intersect at point $M$. Find the y-coordinate of point $M$.

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