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The phrase "cast of thought" is correct and usable in written English with the meaning of to change or divert one's thought or attention to something else.
For example, "After realizing he was taking the wrong approach to the problem, he decided to cast of thought and try a new approach."
Exact(11)
Compelled to act, he is "sicklied o'er with the pale cast of thought".
Moreover, like his oeuvre as a whole, it is, to quote the most famous, most melancholy of Danes, "sicklied o'er with the pale cast of thought".
Otherwise, Mr. Asprey's Hamlet is too impatient to convince as a vacillating philosopher prince, whose resolution is "sicklied o'er with the pale cast of thought".
"Oh, it's my father's hand still on me — casting over my social relations not the pale cast of thought, but the pale cast of an inhibited deference to an unexamined undiscriminating 'niceness' toward everyone" — he's fifty-seven.
Though his customary serious manner was tinged with humour, he was not persuasive and could irritate a questioner with the brusqueness of his statements, his theoretical cast of thought, and the suppressed irony of his half smile.
Like all men of a bold and original cast of thought, he rejected established guides and models, cast away conventional forms, and struck one into new and untrodden paths.
Similar(49)
You see the cast of his thought.
It is a world where women crackle with life force and men are sicklied over by the pale cast of scientific thought.
I hope my proposal will not become sicklied over with the pallid cast of second thoughts.
Not alone by his books, sermons, and help to organized movements did Gibbons exercise his zeal for the spread of God's p213 word, but by his daily contact with men, by his bearing, by the cast of his thoughts, and even by his choice of words in ordinary conversation.
As Computational Intelligence (CI) techniques evolved, a number of frameworks emerged; such as Recognition-Primed Decision (RPD), Pro- cedural Reasoning System (PRS), Collaborative Agent for Simulating Teamwork (CAST), Adaptive Character of Thought– Rational (ACT-R), distributed Multi-Agent Reasoning System (dMars), State, Operator And Result (SOAR) and Java Agent Compiler and Kernel (JACK).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com