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The phrase "agrees to cooperate" is correct and usable in written English.
It can be used in contexts where one party is expressing their willingness to work together with another party.
Example: "After several discussions, the two companies finally agrees to cooperate on the new project."
Alternatives: "consents to collaborate" or "commits to working together."
Exact(10)
Iran agrees to cooperate fully with the IAEA and suspend all uranium enrichment.
They will let her go only if she agrees to cooperate with them.
At first, the killer welcomes the publicity, but when Eve agrees to cooperate with the police in a news blackout, he turns on her.
Peruvian prosecutors said they would seek a sentence of life in prison for the former spy chief, but they have hinted that they may be more lenient if he agrees to cooperate in other investigations.
The prosecutors have dangled before her more lenient treatment if she agrees to cooperate in the prosecution of other members of the radical group, in particular in a bank robbery near Sacramento in 1975 in which a bystander, a mother of four, was killed.
Make sure the agreement includes a "further assurances" clause, in which the employee agrees to cooperate in the future, if needed, to assist with showing that the startup owns the IP.
Similar(44)
Ultimately, 11 agreed to cooperate.
By contrast, Mr. Russert agreed to cooperate.
Both agreed to cooperate with investigators.
Andorra has agreed to cooperate in cross-border fraud investigations.
And Russia agreed to cooperate, sharing intelligence and radar.
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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