
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 $PQR,$ where $p = 8,$ $q = 10,$ and $r = 6.$  Let $J$ be the incenter.

Then
\[\overrightarrow{J} = x \overrightarrow{P} + y \overrightarrow{Q} + z \overrightarrow{R},\] where $x,$ $y,$ and $z$ are constants such that $x + y + z = 1.$  Enter the ordered triple $(x,y,z).$

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