$1.$ Propose a state space and state representation $($data structure$)$

$2.$ Identify the problem type, deterministic or nondeterministic, observable or non$-$observable or fully observable or partially observable

$3.$ Design actions, initial state, goal state, path cost

$4.$ Choose one distinct search strategy and write a program to implement your strategy

$5.$ Discuss the properties: completeness, time complexity, space complexity, and optimality

There are two jugs, one holding $3$ and the other $5$ gallons of water. A number of things can be done with the jugs: they can be filled, emptied, and dumped one into the other either until the poured$-$into jug is full or until the poured$-$out$-$of jug is empty. Devise a sequence of actions that will produce $4$ gallons of water in the larger jug. $($Hint: use only integers.$)$