Catherine the Great implemented several strategies to expand Russia's empire, and among the options provided, the following statements are accurate:
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Catherine defeated the Ottoman Turks to gain a port on the Black Sea. - This is true; her military campaigns in the late 18th century helped secure territories along the Black Sea.
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Catherine fought a war with Sweden to gain access to the Baltic Sea. - This is also true; the Great Northern War and later conflicts helped solidify Russian access to the Baltic Sea.
Therefore, both of these statements regarding her military actions are correct in the context of expanding Russia’s empire.
The other statements, while related to her reign, do not specifically pertain to techniques she employed to expand the empire. The "Table of Ranks" was introduced to create a meritocratic system but was not a direct military action to expand territory. Drafting peasants into the army was a common practice but wasn't a targeted strategy for empire expansion in the context of the question.