
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 $p = 6$, $q = 8$, and $r = 3$. Let $J$ be the incenter of this triangle. Determine the barycentric coordinates of $J$ relative to vertices $P$, $Q$, and $R$, given in the form $\overrightarrow{J} = x\overrightarrow{P} + y\overrightarrow{Q} + z\overrightarrow{R}$ where $x + y + z = 1$.

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