
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 $DEF$, where $DE = 10$, $EF = 8$, and $FD = 6$. Let $J$ be the incenter of triangle $DEF$. Represent the position vector of $J$, denoted as $\overrightarrow{J}$, in terms of the position vectors of the vertices of the triangle, i.e., $\overrightarrow{D}, \overrightarrow{E}, \overrightarrow{F}$ like so: 
\[
\overrightarrow{J} = p \overrightarrow{D} + q \overrightarrow{E} + r\overrightarrow{F}
\]
where $p$, $q$, and $r$ are constants such that $p + q + r = 1$. Find the ordered triple $(p, q, r)$.

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