Cause is simply what created the situation. Reason is the logical explanation of how the situation happened (which may not always be true or honest!).

You can think 'cause' as a 'factor' which causes the case. There may a lot of causes that can make a thing happened. (cause also is a verb ). As Peachey said, reason is a logical explanation that explain how the thing happened and why you did a thing.

reason-理由 cause-原因