verb (v)

• come up with (an idea, plan, explanation, theory, or principle) after a mental effort(verb.creation)

  Example:
  Excogitate a way to measure the speed of light.
  

  Synonym:
  contrive, devise, forge, formulate, invent
  

  source: wordnet30
• reflect deeply on a subject(verb.cognition)

  Example:
  The scientist must stop to observe and start to excogitate.
  

  Synonym:
  chew over, contemplate, meditate, mull, mull over, muse, ponder, reflect, ruminate, speculate, think over
  

  source: wordnet30
• To think out; to find out or discover by thinking; to devise; to contrive.(verb)

  source: webster1913
• To cogitate.(verb)

  source: webster1913