He confirmed he has asked Labour's Ann Clwyd, MP for the Cynon Valley, to examine how NHS hospitals could deal with complaints better in future.
In December, she criticised the care given to her late husband at Cardiff's University Hospital of Wales.
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The charity warns it expects a rise in abandonments as Christmas approaches.
Questions to the First Minister
The tree was blown down in a gale in February after standing for more than 200 years.