
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
The coordinates of the 3 vertices of triangle are \( P(-8, 5) \), \( Q(-15, -19) \), and \( R(1, -7) \). Find the equation of the angle bisector of \(\angle P\) and express it in the form \(ax + by + c = 0\), where \(a, b, c \in \mathbf{Z}^{+}\) and \((a, b, c)=1\), and then calculate \(a + c\).

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