A small, $5\mathrm{.}09-$mm$-$tall bee sits on the principal axis $12\mathrm{.}3$ cm in front of thin lens A $,$ which has focal length $6\mathrm{.}69$ cm $.$ Behind lens A there is another thin lens B with a focal length of $25\mathrm{.}7$ cm $.$ The two share a common principal axis, and are $62\mathrm{.}5$ cm apart.

$($a$)$ How far from lens B is the final image of the bee located?

$($b$)$ What is the height of the bee's image?