
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 rectangle with adjacent side lengths $3$ and $4$. Calculate the sum of the distances from one vertex to the midpoints of each of the rectangular sides.
A) $3 + 2\sqrt{13}$
B) $3.5 + \sqrt{13} + \sqrt{18}$
C) $3.5 + \sqrt{13} + \sqrt{18.25}$
D) $4.5 + \sqrt{13} + \sqrt{18.25}$

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