
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
A square has side length 4 units. Calculate the sum of distances from the bottom-left vertex of this square to the midpoints of each side.
A) \(4 + 2\sqrt{5}\)
B) \(4 + 4\sqrt{5}\)
C) \(8 + 4\sqrt{5}\)
D) \(4\sqrt{5}\)

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