
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
Ita wishes to determine the Fermat point of $\triangle DEF$, where $D$ is at the origin $(0,0)$, $E$ is at $(10,0)$, and $F$ is at $(7,5)$. She assumes that the potential Fermat point $P$ is at $(4,2)$. Calculate the sum of the distances from $P$ to each vertex of $\triangle DEF$.

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