<|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
 In triangle $\triangle ABC$, $\angle C=50^{\circ}$. With point $C$ as the center, draw an arc with a suitable length as the radius, intersecting $AC$ at point $M$ and $BC$ at point $N$. With $M$ and $N$ as centers, draw arcs with lengths greater than $\frac{1}{2}MN$ as the radius. These two arcs intersect at point $D$. Connect $CD$. Find the degree of $\angle ACD$. Express your answer in degrees as a whole number. 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
25
In triangle $\triangle ABC$, $\angle C=50^{\circ}$. With point $C$ as the center, draw an arc with a suitable length as the radius, intersecting $AC$ at point $M$ and $BC$ at point $N$. With $M$ and $N$ as centers, draw arcs with lengths greater than $\frac{1}{2}MN$ as the radius. These two arcs intersect at point $D$. Connect $CD$. Find the degree of $\angle ACD$. Express your answer in degrees as a whole number.
test