
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 line $l$ passing through the focus $F$ of the parabola $C: x^{2}=4y$ intersects the parabola $C$ at points $A$ and $B$, and intersects the circle $x^{2}+y^{2}-2y=0$ at points $M$ and $N$, with points $A$ and $M$ lying on the same side of the $y$-axis, find the value of $|AM|\cdot |BN|$.

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