These two plants are raising my "this is a weed and get rid of it now" alarms. But I grow so many different flowers that I fairly often yank out perfectly good flowers thinking they are weeds. So I thought I'd check first.

The first is the heart-shaped leaf with a red stem

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And the second is those little pointy fern-looking guys

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Should I head out and dig them up? If so, will hand-digging be enough?