
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 $p = 8$, $q = 6$, and $r = 10$. Let $J$ be the incenter of triangle $PQR$. Determine the coordinates of $J$ as a weighted sum of the vertices' coordinates, such that $\overrightarrow{J} = u\overrightarrow{P} + v\overrightarrow{Q} + w\overrightarrow{R}$, where $u, v, w$ are constants satisfying $u + v + w = 1$.

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