
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
Consider a square with vertices labeled as $A$, $B$, $C$, and $D$. The side length of the square is $4$ units. We need to calculate the sum of the distances from vertex $A$, which is positioned at the origin $(0,0)$, to the midpoints of each side of the square.
A) $4 + 4\sqrt{2}$
B) $4 + 4\sqrt{3}$
C) $4 + 4\sqrt{4}$
D) $4 + 4\sqrt{5}$
E) $4 + 4\sqrt{6}$

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