Consider the following blocks$-$world problem: There are three blocks, named a$,$ b and c$,$ and three places, numbered $1,2$ and $3.$ The initial state is given by the following list:

$[$clear$($c$),$clear$(2),$clear$(3),$on$($a$,1),$on$($b$,$a$),$on$($c$,$b$)]$

Use the following assumptions in your answers to the questions given below:

$($i$)$ The add$-$Iist for action move$($X$,$ From, To$)$ is $[$on$($X$,$To$),$clear$($From$)].$

$($ii$)$ The delete$-$list for action move $($X$,$ From, To$)$ is $[$ on $($X$,$ From$),$ c$1$ ear $($To$)].$

$($iii$)$ The preconditions for action move$($X$,$ From, To$)$ are $[$clear$($X$),$clear$($To$),$ on$($X$,$ From$).$

$($iv$)$ Always select the leftmost goal in the goal list, eg when a clear $()$ fact needs to be selected from the state space, the one that occurs first in the state space will be selected.