
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 the parabola $C_{1}: x^{2}=2py (p > 0)$ and the circle $C_{2}: x^{2}+y^{2}=5$, the distance between the two intersection points is $4$.  
(I) Find the value of $p$;  
(II) Let a line passing through the focus $F$ of the parabola $C_{1}$ with a slope of $k$ intersect the parabola at points $A$ and $B$, and intersect the circle $C_{2}$ at points $C$ and $D$. When $k \in [0,1]$, find the range of values for $|AB| \cdot |CD|$.

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