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The phrase "a complementary task" is correct and usable in written English.
You can use it to refer to a task that enhances or completes another task, often in a collaborative or supportive context.
Example: "In our project, I will handle the data analysis while you take on a complementary task of creating the presentation."
Alternatives: "an auxiliary task" or "a supportive task".
Exact(1)
Forming a model description language, the MCL is combined with a complementary task execution language (TEL), which describes how the input from the MCL will be used to generate a desired output.
Similar(59)
Via a phenomenon called complementary task specialization, an increase in the number of non-English speaking immigrants who specialize in manual labor jobs pushes Americans who speak English but have few other skills into higher paid jobs that require communication.
Since in the discussion we will return to this sensor evolution scenario in a broader context, we briefly conclude the section by mentioning the results from [57] concerning the complementary task of evolving actuators which maximize empowerment for a fixed sensor.
Meanwhile he was grievously wanting in that other great, complementary task - the building of his state in the making.
In manufacturing, for example, robots are evolving from potentially dangerous and "dumb" industrial machines into smart, context-aware "cobots". A cobot arm might, for example, handle repetitive actions that require heavy lifting, while a person performs complementary tasks that require dexterity and human judgment, such as assembling a gear motor.
Any feature based approach can be divided into two complementary tasks: an interest point detector [19], [20] and a descriptor encoding information from a local patch of the image at this location, that can be based on histograms [3], [21], spatial frequency [22] [24], local derivatives [25] [27], steerable filters [28], or invariant moments [29].
When we build a team to direct a project successfully, we assess complementary tasks to our team members.
As the share of tasks completed by labour falls, any given technological change is more likely to appear to be labour-substituting, since the share of workers that could potentially benefit from the change as a result of working on complementary tasks keeps dropping.We don't want to force workers out of the labour force.
Despite that, reusing a task often involves reusing complementary tasks.
Data suggest that the collaborating firms that specialize in a particular function have access to others in the systems performing complementary tasks and this creates a level playing field within the network.
And yet the library remained principally a place where books, in all their various forms, were stored for consultation and preservation of "ancient traditions or notions 'gray with time'". Other institutions fulfilled other complementary tasks necessary in a civilized society: hospitals, philanthropic associations, guilds.
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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