We have a right triangle $\triangle ABC$ where the legs $AB$ and $BC$ have lengths $6$ and $3\sqrt{3},$ respectively. Medians $AM$ and $CN$ meet at point $P.$ What is the length of $CP$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
We have a right triangle $\triangle ABC$ where the legs $AB$ and $BC$ have lengths $6$ and $3\sqrt{3},$ respectively. Medians $AM$ and $CN$ meet at point $P.$ What is the length of $CP$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
We have a right triangle $\triangle ABC$ where the legs $AB$ and $BC$ have lengths $6$ and $3\sqrt{3},$ respectively. Medians $AM$ and $CN$ meet at point $P.$ What is the length of $CP$?
train