A ball is dropped from $405$ meters and rebounds two-thirds the distance it falls each time it bounces. How many meters will the ball have traveled when it hits the ground the fourth time?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A ball is dropped from $405$ meters and rebounds two-thirds the distance it falls each time it bounces. How many meters will the ball have traveled when it hits the ground the fourth time?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1545
A ball is dropped from $405$ meters and rebounds two-thirds the distance it falls each time it bounces. How many meters will the ball have traveled when it hits the ground the fourth time?
train