
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
Calculate the sum of the distances from one vertex of an equilateral triangle to the midpoints of each of the sides where each side is 3 units long.
A) $3 + 9\sqrt{3}$
B) $3 + \frac{3}{2} \sqrt{3}$
C) $3 + \frac{9}{2} \sqrt{3}$
D) $3 + 4\sqrt{3}$
E) $3 + 6\sqrt{3}$

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