
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 a parabola $C: x^2 = 2py$ ($p > 0$), a line $l$ with a slope of $1$ passes through its focus and intersects the parabola $C$ at points $M$ and $N$, and $|MN| = 16$.
(Ⅰ) Find the equation of the parabola $C$.
(Ⅱ) A moving circle $P$ with its center on the parabola $C$ passes through a fixed point $D(0, 4)$. If the circle $P$ intersects the x-axis at points $A$ and $B$, and $|DA| < |DB|$, find the minimum value of $\frac {|DA|}{|DB|}$.

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