A horizontal circular platform rotates counterclockwise about its axis at the rate of $0\mathrm{.}957$ rad$/$s$.$ You, with a mass of $65\mathrm{.}3$ kg$,$ walk clockwise around the platform along its edge at the speed of $1\mathrm{.}13$ m$/$s with respect to the platform. Your $20\mathrm{.}7$ kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your $18\mathrm{.}3$ kg mutt, on the other hand, sits still on the platform at a position that is $3/4$ of the platform's radius from the center. Model the platform as a uniform disk with mass $90\mathrm{.}9$ kg and radius $1\mathrm{.}97$ m$.$ Calculate the total angular momentum L tot of the system.