<|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
 Given three non-collinear plane vectors $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$, with equal angles between each pair. If $|\overrightarrow{a}|=|\overrightarrow{b}|=2$ and $|\overrightarrow{c}|=1$, then find the magnitude of $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$. 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
1
Given three non-collinear plane vectors $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$, with equal angles between each pair. If $|\overrightarrow{a}|=|\overrightarrow{b}|=2$ and $|\overrightarrow{c}|=1$, then find the magnitude of $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$.
test