
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: $y^{2}=2px (p > 0)$, its focus is $F$, and point $A(m,2) (m > 1)$ is a point on the parabola, satisfying $|AF|= \frac {5}{2}$.
(1) Find the equation of the parabola;
(2) Given $M(-2,0)$, $N(2,0)$, the line passing through $N$ intersects the parabola at points $C$ and $D$. If $S_{\triangle MCD}=16$, find the equation of the line $CD$.

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