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

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