"proceeded to read" is a correct and usable phrase in written English.
You could use this phrase in a variety of contexts. For example, "After receiving her book, she proceeded to read it cover to cover."
He proceeded to read from his forthcoming collection of prose pieces and smiled each time the word "nothing" appeared.
Clasping a replica of a 1775 flag, which bore the credo "Appeal to Heaven," Mr. Manship proceeded to read aloud the Preamble of the Constitution.
He showed a piece of paper with the number and proceeded to read the digits out loud twice, adding, "Give it a shot.
He proceeded to read an "indictment" against the former secretary of state, asking delegates after each charge whether she was guilty or not guilty.
Somewhat miffed, Fuller gained an audience with the man and proceeded to read the paper aloud to him in carefully metered doses, watching his face to make sure that each portion was understood before he went on to the next.
And yet, barely in her mid-20s and already with three small children, she took herself off to the local library and proceeded to read her way through it.
He then proceeds to read my college transcript: "Bovine Psychology, B-minus; Topics in Needlepoint, C-plus..."...
He then proceeds to read my college transcript: "Bovine Psychology, B-minus; Topics in Needlepoint, C-plus......
She proceeds to read aloud from her mother's book in an attempt to oust the sleeping woman from the room.
"I hope you don't mind that this is a little presumptuous on my part," a deferential Dirksen said, proceeding to read aloud a copy he had already drafted.
Every day, after digesting the obits in the Morning News — clipping and filing the ones she might want to refer to later on — she proceeds to read the obituary pages of the Times, the Washington Post, the Fort Worth Star-Telegram, the Houston Chronicle, the Archer County (Texas) News, and the Electra (Texas) Star-News.
