
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
Determine the sum of distances from point $P = (5,1)$ to the vertices of $\triangle ABC$, where $A = (0,0)$, $B = (8,0)$, and $C = (4,6)$. Express the sum in the form $x\sqrt{a} + y\sqrt{b}$, where $x$ and $y$ are integers, and find $x + y$.

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