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The phrase "a new task of" is correct and usable in written English.
It can be used when introducing or describing a specific responsibility or assignment that is being assigned or undertaken.
Example: "The team has been assigned a new task of developing a marketing strategy for the upcoming product launch."
Alternatives: "a new assignment to" or "a new responsibility for".
Exact(3)
A new task of paired position-learning was designed, based on the A B A C paradigm, which was used in paired word learning.
The distinction between appearance and reality, as expressed in the propositional copula, then leads dialectically to a new task of thought, the task of theoretical science, of systematic inquiry into the realm of truths.
A new task of the Güell-López's for Comillas was the gazebo for Alfonso XII's visit to the Cantabrian town in 1881.
Similar(57)
More prosaically, a new task force of landlords and bank officials is assessing what to do with indebted properties.
Dynamically occurring events are taken into account when planning, including introduction of a new task or change of task options, failure of a satellite or means of communication.
At some later point, the existing structure was co-opted for a new task, the expulsion of words out into the world.
They students also display insecurity in engaging in a new task, in anticipation of having to redo assignments several times during their work at the project.
Recently, Governor Andrew Cuomo convened a new task force, consisting of leaders from the state's top HIV/AIDS service organizations, to end AIDS in New York State.
Operating in a whisky-centric region was difficult, and he developed a new "task force" approach of sending more missionaries to a single location at a time; this successfully drew local press attention and several hundred new recruits.
A new task replaces one of the existing tasks on day 6 and every 5th day after this.
In August, Mayor Michael R. Bloomberg appointed William Solecki co-chairman of a new task force, the New York City Panel on Climate Change.
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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