"keen to act" is correct and usable in written English.
You can use it when you want to express enthusiasm to do something. Example: The actor was keen to act in the new movie.
He is keen to act on France's poor record on race equality before Barack Obama takes office in January.
Why, when her grandmother was so obsessed with social respectability, was she herself so keen to act out a life of complete freedom from conventional mores?
Ministers are keen to act because they believe that the Westminster and Holyrood governments sailed close to the wind in the Scottish referendum.
When Slobodan Milosevic's Serbian government embarked on a similar policy of ethnic cleansing in Kosovo, Blair decided that he had to step in: "Why was I so keen to act?
Eileen Claussen of the Pew Centre, which represents many big businesses keen to act on climate change, said Mr Bush's new strategy was just an effort to cloak "business as usual" in some kind of finery.
State pensions, which already absorb 12% of GDP, may well eat up 20% by 2040 if nothing is done.The government talks of reform, but does not seem too keen to act.
However Joorabchian believes Tevez has always acted professionally and is keen to play football.
Glastonbury founder Michael Eavis has defended Metallica's right to be this year's headline act, saying no band has been as "keen" to play at the festival.
Many are keen to move into Europe.
But if you're keen to be in France during the tournament it makes sense to act ahead of the draw.
