
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 \(XYZ\), sides are given by \(x = 8\), \(y = 11\), and \(z = 5\). Let \(J\) be the incenter of triangle \(XYZ\).

Determine the position vector \(\overrightarrow{J}\) in terms of \(\overrightarrow{X}\), \(\overrightarrow{Y}\), and \(\overrightarrow{Z}\), such that \(\overrightarrow{J} = p \overrightarrow{X} + q \overrightarrow{Y} + r \overrightarrow{Z}\), where \(p\), \(q\), and \(r\) are constants with \(p + q + r = 1\). Calculate the ordered triple \((p, q, r)\).

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