A geologist is searching for a mineral specimen with a specific density of 8.4 g/cm³ from a sorted list of 11 measured densities:

$$[2.1,2.8,3.5,4.2,4.9,5.6,6.3,7.0,7.7,8.4,9.1]$$

Using the binary search algorithm with indices 1 to 11, and calculating the midpoint index using the formula $\lfloor \frac{L+R}{2}\rfloor$ (where $L$ and $R$ represent the lower and upper bounds of the current search space), demonstrate how the target density of 8.4 g/cm³ is located. For each step, identify the midpoint index and its value, show the comparison with the target, and state the remaining list of densities.