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$($a$),$ clear$($c$),$ clear$($d$),$ clear$(3),$ on$($a$,1),$ on$($b$,2),$ on$($c$,$b$),$ on$($d$,4)]$

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

$($i$)$ The add$-$list 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$),$ clear$($To$)].$

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

$($vi$)$ Always select the leftmost goal in the goal list.

Note that we follow the convention used by Bratko: After an action has been completed, the elements in the state space $($if present$)$ have the following sequence:

$[$clear$($a$),...,$clear$($c$),$clear$(1),...,$clear$(3),$on$($a$,?),...,$on$($c$,?)]$

Give the sequence of moves that a simple means$-$ends planner will generate to achieve the goal on$($b$,1)$ from the given initial state. Give the preconditions of each proposed action as well as the subgoal that each action in the plan achieves.