
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 $DEF,$ $d = 8,$ $e = 15,$ and $f = 17.$ Let $J$ be the incenter.

Find the barycentric coordinates (x, y, z) such that
\[\overrightarrow{J} = x \overrightarrow{D} + y \overrightarrow{E} + z \overrightarrow{F},\]
where $x + y + z = 1.$

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