Fetching details from the dictionary...

as much as possible; as far as possible; to the best of one's ability; diligently
努めて冷静に対応するよう心がけている状況なのだ。
I'm trying to respond as calmly as possible.
健康のために努めて野菜を多く摂取するようにしている。
For health, I try to eat as many vegetables as possible.
努めて笑顔を絶やさないよう意識して生活していた。
I consciously try to always keep a smile in my life.