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There is an $S^1$-action on the Quaternionic projective plane $\mathbb{H}\mathbb{P}^2$ with exactly 3 fixed points. They are not hard to construct (done in a similar way to the standard $S^1$-actions on $\mathbb{C}\mathbb{P}^2$) but the details of such an action are contained here https://arxiv.org/pdf/1303.2351.pdf.