
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 square wherein each side has a length of $4$. What is the sum of the distances from one vertex of this square to the midpoints of each of the sides of the square?
A) \(8\sqrt{2}\)
B) \(4+4\sqrt{5}\)
C) \(8\sqrt{3}\)
D) \(4\sqrt{2}\)
E) \(8\sqrt{5}\)

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