
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
Wanda is trying to locate the Fermat point $P$ of $\triangle ABC$, where $A$ is at the origin, $B$ is at $(8,0)$, and $C$ is at $(4,7)$. She guesses that the point is at $P = (3,3)$, and computes the sum of the distances from $P$ to the vertices of $\triangle ABC$. If she obtains $a\sqrt{b} + c\sqrt{d}$, where $a, b, c, d$ are integers, what is $a + c$?

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