
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 $C$: $x^{2}=2py (p > 0)$ with its focus $F$, the point $P$ intersects with the $x$-axis on line $x=4$, and the point $Q$ intersects with the parabola $C$. Moreover, $|QF|= \frac {5}{4}|PQ|$.
(I) Find the equation of $C$;
(II) Point $A(-a,a) (a > 0)$ is on the parabola $C$. Determine whether there exists a line $l$: $y=kx+4$ intersecting with $C$ at points $M$ and $N$, such that $\triangle MAN$ is a right triangle with $MN$ as its slanted edge. If such a line exists, find its equation; otherwise, provide an explanation.

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