In the excerpt from President Washington's Farewell Address, his purpose can be identified as:
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To express his concern for his country's future - Washington emphasizes the importance of the upcoming election and indicates that his decision to decline re-election is made with careful consideration for the nation’s well-being.
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To announce that he will not seek a third term - The primary purpose of the excerpt is to inform the public of his decision not to be considered for re-election to the Executive Government.
These two choices align with the overall intent and message of Washington's speech.