
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 focus $F$, the point $H$ is the intersection of the line $x=4$ with the $x$-axis, and the point $Q$ is the intersection of the line $x=4$ with $C$. It is also given that $|QF|= \frac {3}{2}|HQ|$.
(1) Find the equation of $C$;
(2) A line $l$ passing through $F$ intersects $C$ at points $A$ and $B$. Lines $l_{1}$ and $l_{2}$ pass through $A$ and $B$, respectively, and are tangent to $C$. These two lines intersect at point $R$. Find the minimum value of $S_{\triangle RAB}$.

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