Given that a sequence satisfies $x_0=0$ and $|x_k|=|x_{k-1}+3|$ for all integers $k\ge1$, find the minimum possible value of $|x_1+x_2+\cdots+x_{2006}|$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Given that a sequence satisfies $x_0=0$ and $|x_k|=|x_{k-1}+3|$ for all integers $k\ge1$, find the minimum possible value of $|x_1+x_2+\cdots+x_{2006}|$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
27
Given that a sequence satisfies $x_0=0$ and $|x_k|=|x_{k-1}+3|$ for all integers $k\ge1$, find the minimum possible value of $|x_1+x_2+\cdots+x_{2006}|$.
train