The word 'beat' and 'embrace'

(1)The word ' ' means to do or be better than a record or score.

(2)The word' ' means to accept a belief, theory, or change willingly

I think the words in the blanks is 'beat' and 'embrace'. right?

Here is the question.

Is 'improve' ok in the first blank? And 'agree' is ok in the second?

Thanks in advance.