Is the sentence in the title absolutely grammatically correct? I recently had an argument with a fellow student, and he said that the sentence is incorrect. I do not think he is right, because I saw numerous examples of such constructions on the Internet, but we were never taught to use such constructions, so I decided to ask here to be sure.
Here are some similar sentences that I just found on the Internet as examples:
(1) I am tired and thinking in circles. (From An Unreasonable Woman: A True Story of Shrimpers, Politicos, Polluters, and the Fight for Seadrift, Texas by Diane Wilson)
(2) And because I am tired and doing what I do not want to be doing, it takes another minute or two before the date sinks in. (From Man in the Moon: Essays on Fathers and Fatherhood by Stephanie G'Shwind)
(3) Where were you born? Melbourne, Australia ... What do you want to be when you grow up? I am grown up and doing what I want to be doing, Teaching! (Source)