The objective of this problem is to understand a timed automaton, and then to modify it as specified.

$($a$)$ For the timed automaton shown below, describe the output $\backslash ($ y $\backslash ).$ Avoid imprecise or sloppy notation.

$($b$)$ Assume there is a new pure input reset, and that when this input is present, the hybrid system starts over, behaving as if it were starting at time $0$ again. Modify the hybrid system from part $($a$)$ to do this.

please hand write the solution in detailed steps. Thank you!