Markov decision process: Given the car racing model as shown below $($i$.$e$.,$

example from slides$),$ assume each state's starting value is $0($i$.$e$.,V_0(s)=0),$ if the

state value discount $($i$.$e$.,)$ by $0\mathrm{.}9$ after each action step, calculate: $(1)$ the optimal

values that you can gain after $3$ steps $($iterations$)$ if starting from the "Cool" state and

the "Warm" state respectively, i$.$e$.,V_3(Cl)$ and Warm$).(2)$ if keep racing the car

$($i$.$e$.,$ taking action$),$ will the optimal values of the two states converge? If yes, what

are the values, i$.$e$.,V^{**}(Cl)$ and $V^{**}(Warm)?(3)$ Based on your calculation, what's

the optimal policy in this car racing model, i$.$e$.,{}^{**}(Cl)$ and Warm$)?$