Synonyms of 'cherish'
1 cling to
I will cherish the memory of that visit for many years to come.
2 care for
He genuinely loved and cherished his children.
He cherished an ambition to be an actor.
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If you entertain an idea or suggestion, you allow yourself to consider it as possible or as worth thinking about seriously.
I wouldn't entertain the idea of doing such a job.
Thesaurus for cherish from the Collins English Thesaurus
If you cherish something such as a hope or a pleasant memory , you keep it in your mind for a long period of time.