Natalie has a copy of the unit interval $[0,1]$ that is colored white. She also has a black marker, and she colors the interval in the following manner: at each step, she selects a value $x\in [0,1]$ uniformly at random, and 

(a) If $x\leq\tfrac12$ she colors the interval $[x,x+\tfrac12]$ with her marker.

(b) If $x>\tfrac12$ she colors the intervals $[x,1]$ and $[0,x-\tfrac12]$ with her marker.

What is the expected value of the number of steps Natalie will need to color the entire interval black?

Let's think step by step and output the final answer within \boxed{}.
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