Think, cogitate, reflect, reason, speculate, deliberate can all mean to use one’s powers of conception, judgment, or inference in regard to any matter or subject which concerns one or interests one.
Think is the general term implying mental activity for the sake of forming ideas or of reaching conclusions; the term need not suggest closeness of application, clearness in the ideas formed, or correctness in the conclusions reached, though when used without qualification it often does suggest the attainment or approximation of these.
Cogitate places more stress on the process than upon the results of thinking; it is often used to suggest the appearance or the atmosphere of profound but not necessarily productive thinking.
Reflect usually implies a turning of one’s thoughts back upon or back to something that exists, has occurred, or needs reexamining; it implies quiet, unhurried, and serious consideration or study.
Reason implies consecutive logical thought, beginning with a postulate, a premise, or definite data or evidence and proceeding through inferences drawn from these to a conclusion or judgment.
Speculate implies the processes of reasoning but stresses either the uncertainty of the premises or the incompleteness of the data and therefore usually imputes a hypothetical or theoretical character to the conclusions reached.
Deliberate suggests slow and careful thought or reasoning and fair consideration of various aspects in an attempt to reach a conclusion often on a matter of public interest.