How to display a three-state and double-action column via material icons?

I have this Boolean field which can be zero too. So, I have three states: null, true, false.

On this basis, I have two actions: make true, make false

Is there a good way to associate UI / UX into one understandable element of the UI?

Right now I have this design. If a field is null, it is displayed as false. If the field is wrong, it is displayed as a material undo icon. If it is true, it is displayed as a control icon. Hovering, if it is false or nil, click to approve would be shown, and in case it is true click to disapprove would be shown.

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These are the problems I have with this design:

  • The cliquability of the elements is not apparent. Thousands of users of my system quickly realize it because I have the consistency
  • The null elements must be displayed differently, and they can not be displayed empty, because empty will not be clickable.

How can I improve this?