
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 sides $AB = 15$, $BC = 16$, and $AC = 17$. The points $P, Q$, and $R$ are the midpoints of $\overline{AB}, \overline{BC}$, and $\overline{AC}$ respectively. Let $Y \neq Q$ be the intersection of the circumcircles of $\triangle BPQ$ and $\triangle CRQ$. What is $YA + YB + YC$?
A) 72
B) 36
C) 45
D) 54
E) 63

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