The coefficients of the polynomial $p(x)$ are all nonnegative integers.  If $p(1) = 4$ and $p(5) = 136,$ then find $p(6).$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The coefficients of the polynomial $p(x)$ are all nonnegative integers.  If $p(1) = 4$ and $p(5) = 136,$ then find $p(6).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
229
The coefficients of the polynomial $p(x)$ are all nonnegative integers.  If $p(1) = 4$ and $p(5) = 136,$ then find $p(6).$
train