<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 A triangle has vertices  $P=(-8,5)$ ,  $Q=(-15,-19)$ , and  $R=(1,-7)$ . The equation of the bisector of  $\angle P$  can be written in the form  $ax+2y+c=0$ . Find  $a+c$ . Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
89
A triangle has vertices  $P=(-8,5)$ ,  $Q=(-15,-19)$ , and  $R=(1,-7)$ . The equation of the bisector of  $\angle P$  can be written in the form  $ax+2y+c=0$ . Find  $a+c$ .
test