simulate mouse movement

Hi,
I am using graphics software (architecture) whose tool palettes are hidden. These appear:
1- when the mouse pointer lands on the header of the palette (see at the 4th second in the video below)
2- or when the mouse touches the edge of the screen.
(see at the 1st second in the video below)

My request is as follows:
1- I would like to simulate the movement of the mouse to a specific point on the screen, using a keyboard shortcut or a key sequence ("ctrl ctrl" for example)
2- I would like to simulate a mouse movement to the left or right edge of the screen, using a keyboard shortcut or a key sequence ("option-option" for example)

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