
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
Triangle $ABC$ has $AB = 15, BC = 16$, and $AC = 17$. The points $D, E$, and $F$ are the midpoints of $\overline{AB}, \overline{BC}$, and $\overline{AC}$ respectively. Let $X \neq E$ be the intersection of the circumcircles of $\triangle BDE$ and $\triangle CEF$. Determine $XA + XB + XC$.
A) $\frac{480 \sqrt{39}}{7}$
B) $\frac{960 \sqrt{39}}{14}$
C) $\frac{1200 \sqrt{39}}{17}$
D) $\frac{1020 \sqrt{39}}{15}$

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