
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 $PQR,$ $p = 8,$ $q = 10,$ and $r = 6.$ Let $J$ be the incenter. Determine the coordinates of $J$ as a combination of the position vectors of $P,$ $Q,$ and $R,$ expressed in the form:
\[\overrightarrow{J} = x \overrightarrow{P} + y \overrightarrow{Q} + z \overrightarrow{R},\]
where $x,$ $y,$ and $z$ are constants such that $x + y + z = 1.$

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