# Create a new child node for the next state, according to `problem`.
	# Used internally by the solvers but made public for those who want to replay a plan.
	#
	# ensure `result.parent == self`
	# ensure `result.action == action`
	fun apply_action(action: A): SearchNode[S, A]
	do
		var new_state = problem.apply_action(state, action)
		var new_cost = problem.cost(state, action, new_state)
		var new_node = new SearchNode[S, A](problem, new_state, self, action, cost + new_cost, depth+1)
		new_node.compute_heuristic
		return new_node
	end