In a geometric sequence $a_1,$ $a_2,$ $a_3,$ $\dots,$ where all the terms are positive, $a_5 - a_4 = 576$ and $a_2 - a_1 = 9.$  Find $a_1 + a_2 + a_3 + a_4 + a_5.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In a geometric sequence $a_1,$ $a_2,$ $a_3,$ $\dots,$ where all the terms are positive, $a_5 - a_4 = 576$ and $a_2 - a_1 = 9.$  Find $a_1 + a_2 + a_3 + a_4 + a_5.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1023
In a geometric sequence $a_1,$ $a_2,$ $a_3,$ $\dots,$ where all the terms are positive, $a_5 - a_4 = 576$ and $a_2 - a_1 = 9.$  Find $a_1 + a_2 + a_3 + a_4 + a_5.$
train