
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
In triangle $ABC$, the side lengths are $AB = 15, BC = 13$, and $AC = 14$. Points $D, E$, and $F$ are the midpoints of sides $\overline{AB}, \overline{BC}$, and $\overline{AC}$ respectively. Another point $X \neq E$ exists as the intersection of the circumcircles of triangles $BDE$ and $CEF$. Determine $XA + XB + XC$.
A) $\frac{195}{8}$
B) $\frac{39}{4}$
C) $\frac{117}{8}$
D) $27\sqrt{2}$
E) $\frac{39}{2}$

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