Very good advice
assuming OP your parents have capacity, the following are all good ideas
1/ split up savings so they are not in joint names, they should be broadly 50/50 to avoid falling foul of deprivation rules.
2/ sever joint tenants to tenants in common
3/ each parent wills their share to the children with a life interest for the survivor
4/ get power of attorney for health and finances
5/ you could consider buying 1% of your parents home from them at market value (£3000 in your case), this would make you a Tennant in common with them, this is a valuable tool, because no DPA charging order can be placed without the signatures of all tenants, this makes sure they don't unwittingly make a bad decision.
6/ when it comes to it, do not sign anything in respect of care until first speaking to a legal professional and reading the sections of the care act on disregarded property - local authority social workers push to get DPAs signed, sadly many people void their right to a mandatory disregard by signing such documents.
DPAs are not always a bad thing, but its a massive thing to sign and people often do it without the full facts.