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The phrase "have worked to" is correct and usable in written English.
You can use it whenever the context implies that someone has taken action to achieve a certain result. For example: "We have worked to make our school more welcoming and inclusive for all students."
Exact(60)
We have worked to strengthen the opposition.
Since then, both sides have worked to resolve their differences.
The lengthy restructuring process may have worked to Kushner's advantage.
Medical professionals have worked to develop vaccines against some of the most important fecal oral pathogens.
We have worked to increase performance with proper data representation and reducing row operations on GPU.
Engineers have worked to restore its structural stability.
More recently, firms have worked to integrate insular technologies into a coherent whole.
With this objective in mind, CPM software developers have worked to improve this modeling capability.
"We have worked to be entertaining but not political.
The group's tactics have worked, to a degree.
Union officials have worked to dispel those concerns.
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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