<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 James the naked mole rat is hopping on the number line. He starts at  $0$  and jumps exactly  $2^{n}$  either forward or backward at random at time  $n$  seconds, his first jump being at time  $n = 0$ . What is the expected number of jumps James takes before he is on a number that exceeds  $8$ ? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
6
James the naked mole rat is hopping on the number line. He starts at  $0$  and jumps exactly  $2^{n}$  either forward or backward at random at time  $n$  seconds, his first jump being at time  $n = 0$ . What is the expected number of jumps James takes before he is on a number that exceeds  $8$ ?
test