
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
- Maya wishes to determine if the point $Q = (3,1)$ minimizes the sum of its distances from the vertices of triangle $DEF$, where $D$ is at (1,1), $E$ is at (7,-2), and $F$ is at (4,5). Calculate the sum of these distances, and express it as $p + q\sqrt{r}$, where $p$, $q$, and $r$ are integers. What is $p + q$?

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