HMMT 2022 U4

For a real number $x$, let $[x]$ be $x$ rounded to the nearest integer and $\langle x\rangle$ be $x$ rounded to the nearest tenth. Real numbers $a$ and $b$ satisfy $\langle a\rangle+[b]=98.6$ and $[a]+\langle b\rangle=99.3$. Compute the minimum possible value of $[10(a+b)]$. (Here, any number equally between two integers or tenths of integers, respectively, is rounded up. For example, $[-4.5]=-4$ and $\langle 4.35\rangle=4.4$.)