
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 $PQR,$ let $p = 8,$ $q = 11,$ and $r = 5.$ Let $J$ be the incenter of the triangle.

Then
\[\overrightarrow{J} = u \overrightarrow{P} + v \overrightarrow{Q} + w \overrightarrow{R},\]where $u,$ $v,$ and $w$ are constants such that $u + v + w = 1.$ Find the ordered triple $(u, v, w).$

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