
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 $PQR$, with side lengths $PQ = 10$, $QR = 24$, and $PR = 26$, has midpoints $A, B$, and $C$ on $\overline{PQ}, \overline{QR}$, and $\overline{PR}$, respectively. Find $YA + YB + YC$, given that $Y \neq B$ is the intersection of the circumcircles of $\triangle QAB$ and $\triangle RBC$.

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