
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, where vertex A is at the origin, vertex B is at (8, 0), and vertex C is at (4, 6), determine the sum of the distances from point P = (5, 3) to each vertex. The sum is expressed as $m\sqrt{a} + n\sqrt{b}$, where $m$, $n$, $a$, and $b$ are integers. Find the value of $m + n$.

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