Given the system shown below, do the following: $(60$ pts $)$

a$.$ Find the asymptotes $($specifically ${}_a$ and ${}_a).(15pts$

b$.$ Sketch the root locus. $(30pts)$

c$.$ Estimate the location of the break$-$in and$/$or the breakaway point$($s$).$ Do not make any calculations, estimate the value$($s$)$ from the root locus sketch. $(10$ pts$)$

d$.$ For which value of $K$ will the system have a closed$-$loop pole at $-5?(5$ pts$)$