Longer problem focused on problem solving multiple steps. This problem will be graded based on process, clarity of work, and correct answer and units.

A member is supported with a ball and socket joint at A $,$ which is aligned with a smooth journal bearing at $B,$ and a ball bearing at $C$ on the $x-y$ plane. If $a=3\mathrm{.}4m,b=5\mathrm{.}2m,F=676N,$ and $M=2\mathrm{.}2kN-m.($moment is around the x $-$axis$)$ Solve for the support reactions at $A,B,$ and C $.$