‘I think that I shall do (A)’, ～ようとしない is a combination of a verb that has been grouped with the 助動詞（じょどうし） (auxiliary verb) う (or よう
), followed by the 格助詞（かくじょし） (case marking particle) と, and then another verb. In this case, する
is often translated as ‘shall not (A)’, but with emphasis on a lack of effort, or willingness.
Since he is angry, he is not willing to listen to what anyone has to say.
He isn't quite trying to go home. (It doesn't seem like he is going to leave anytime soon)
As ～ようとしない implies a lack of effort, this expression is usually quite negative, and mostly refers to other people, rather than the speaker themselves. If ～ようとしない were used to refer to the speaker, it will come across as ‘I shall not do (A)’, which would sound very abrupt/potentially rude. If speaking about yourself, ようと思（おも）
わない may be used instead, meaning ‘I don’t think I shall do (A)’, or ‘I think I shan't do (A)’.
I don't think I would eat it if I had to buy it myself, but I might if someone gave it to me.
I think I shan’t change my personality.