
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
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  $8$ ?

Present the answer in LaTex format: \boxed{Your answer}
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