
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 point A(4,4), if the focus of the parabola $y^{2} = 2px$ coincides with the right focus of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, and there is a point M on the parabola whose projection on the y-axis is point N, find the minimum value of $|MA| + |MN|$.

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