
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 $ABC$, $AB = 13$, $BC = 12$, and $AC = 5$. Circle $P$ is the smallest circle that passes through $A$ and is tangent to $BC$. Let $Q$ and $R$ be the points of intersection, distinct from $A$, of circle $P$ with sides $AB$ and $AC$, respectively. Find the length of segment $QR$.
A) 12  
B) 24  
C) 26  
D) 28  
E) 30

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