Find the smallest $n>3$ such that $(1+2+3+\cdots+n)^2$ is a perfect fourth power.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the smallest $n>3$ such that $(1+2+3+\cdots+n)^2$ is a perfect fourth power.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8
Find the smallest $n>3$ such that $(1+2+3+\cdots+n)^2$ is a perfect fourth power.
train