Cows “chew the cud”. The cud (bolo alimentico) is chewed (rumiando) as part of a cow´s eating habits.
Mortals (mortales) often “chew the cud”. This is figurative (figurativo) and it means that people think about, reflect on (reflexionar sobre) or contemplate (contemplar) things. Perhaps, in Spanish you might say “dar vueltas a las cosas”.
- Mr. Casado has been chewing the cud for some days over the right direction for the PP (…ha estado rumiando por unos días sobre…).
- I have been chewing the cud over the issue for 2 hours (he estado reflexionando sobre el asunto por dos horas).
- Do not decide now. Chew the cud. Advise me in a week´s time.
So, I imagine that you have chewed the cud many times.
If you are preparing for the Cambridge First, Advanced or Proficiency exams, you could start a Cambridge speaking task by saying “that is a challenging question, and I need 3 seconds to chew the cud”. You will get higher marks because of the interesting beginning.