The phrase "its task of" is correct and usable in written English.
You can use it when you need to refer to a specific action or tasks that a subject is responsible for. For example, "The company is well aware of its task of providing excellent customer service."
That's the dilemma faced by the journalist hero of Stephen Frears's new film and it is also, by implication, the problem confronting the drama itself as it embarks on its task of spinning glucose into gold.
That the album is still so relevant today suggests it failed in its task of changing attitudes.
It had carried out its task of mediation and conciliation.
The documentary filmmaker Frederick Wiseman offers an enraptured view of a great cultural institution — London's National Gallery — as it struggles and succeeds in its task of preserving and exhibiting art amid declining government support.
The government body that organises the election is in a mess; it is under-funded and way behind in its task of registering voters.
To what extent did the Foreign Office neglect its task of giving clear advice on foreign policy while it constantly reorganised and rebranded itself at the behest of the Treasury?
It fulfills with its tasks of spatial analysis as a discipline.
"This will allow the court to be quick and efficient in its tasks of doing justice".
However, I do not wish the Prince, or, if you prefer, the state, to invoke any faith in order to accomplish its tasks of governance.
From feeding and breathing tubes to wheelchairs, dialysis machines to cardiac monitors, each technology provides specific benefits, and each has its tasks: of complex cleaning and maintenance, and of emotional acceptance [ 31, 46, 47].
The country may be distracted from its urgent task of revamping its tatty infrastructure and helping the private sector to create jobs.
