Virtual solvability of amenable groups with the ascending chain condition

Let $G$ be a finitely generated amenable residually finite group satisfying the ascending chain condition on closed subgroups. Virtual solvability conjecture. The group $G$ is virtually solvable of finite rank. This question arises from constructions involving semidirect products whose factors are abelian and whose acting groups have infinite ascending chains of subgroups closed in the profinite topology. The source does not provide evidence of a resolution, so the conjecture remains open.