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It's possible to programmatically control the mouse using LabVIEW to click at discrete points on the screen using the LabVIEW Call Library Function Node, and use it to call functions from Windows's user32.dll. Relying on Windows functions like SetCursorPos and Mouse_event, you can simulate a mouse click at a given position on screen.
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ButtonExample.zip contains two VIs showing how to simulate a mouse click on a specific button by creating a reference to a control and using property nodes to extract the coordinates of that control.
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Example code from the Example Code Exchange in the NI Community is licensed with the MIT license.