should a president and vice president die does the secretary of state stand next in line to take over the presidency?

No. The speaker of the House is next in line.

http://usgovinfo.about.com/library/weekly/aa010298.htm

Yes, if both the president and vice president were to die, the secretary of state would be next in line to take over the presidency. The presidential line of succession in the United States is outlined in the Presidential Succession Act.

To determine who takes over in the event of the president's and vice president's deaths, here are the necessary steps:

1. Start by consulting the Presidential Succession Act. This law provides a specific order of individuals who would assume the presidency in case of a vacancy. The most recent version of this act was passed in 1947.

2. According to the act, after the vice president, the next in line is the speaker of the House of Representatives. If the speaker is unable or unwilling to assume the office, the succession moves to the president pro tempore of the Senate.

3. If both the speaker of the House and the president pro tempore are unavailable or unable to become president, the line of succession continues through the cabinet positions in the order in which they were created. The secretary of state, who is typically the highest-ranking cabinet position, is next in line.

However, it's important to note that the specific order of succession may change if Congress amends the Presidential Succession Act or if there are changes in the cabinet positions. It is ultimately the responsibility of Congress to determine the order of succession.