
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
Let \(ABC\) be a triangle with \(AB = 13\), \(BC = 14\), and \(CA = 15\). Company XYZ wants to locate their base at the point \(P\) in the plane minimizing the total distance to their workers, who are located at vertices \(A\), \(B\), and \(C\). There are 1, 5, and 4 workers at \(A, B\), and \(C\), respectively. Find the minimum possible total distance Company XYZ's workers have to travel to get to \(P\).

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