President Park's approval rating is at a record low of five percent. Now, the question is, what's next for her? A president's impeachment requires two-thirds of parliament. Park's ruling Saenuri Party holds 122 of the 299 seats.

The party, together with the opposition and influential governors, have urged Park to form a national unity government. Key appointments would be selected by the ruling and opposition camps. That would have weakened the president's hold on government.

But Park has made the first move. She unexpectedly named a new prime minister on Wednesday. She wishes to hand over internal administration but keep control over foreign and security affairs.