
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
Bob chooses a  $4$ -digit binary string uniformly at random, and examines an infinite sequence of uniformly and independently random binary bits. If  $N$  is the least number of bits Bob has to examine in order to find his chosen string, then find the expected value of  $N$ . For example, if Bob’s string is  $0000$  and the stream of bits begins  $101000001 \dots$ , then  $N = 7$ .

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