What is the difference between Assume and Presume?

What is the difference between Assume and Presume? :

Assume :

1 ) Accept something as true before there is proof

I cannot assume anything in this case.

We are assuming that the present situation is going to continue.

2 ) Put on or display something falsely – pretend

He assumed ignorance of the accident.

The look of innocence she assumed had us all fooled.

She assumed an air of great concern for my safety.

3 ) Take on – undertake – begin to act in or exercise something

He will assume his new responsibilities next week.

The problem is beginning to assume massive proposition.

Presume :

1 ) Suppose something to be true – take something for granted

I presume that an agreement will eventually be reached.

Ten passengers are missing, presumed dead.

2 ) Venture to do something – be so bold as to do something

May I presume to advise you?

I shall not presume to disturb you.

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