
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 $DEF$, $d = 5$, $e = 8$, and $f = 6$. Let $J$ be the incenter of triangle $DEF$.

Then
\[\overrightarrow{J} = u \overrightarrow{D} + v \overrightarrow{E} + w \overrightarrow{F},\] where $u, v, w$ are constants such that $u + v + w = 1.$ Determine the ordered triple $(u, v, w)$.

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