If-statement issues with Tic Tac Toe

I'm currently working on writing a script for a Tic Tac Toe game but am running into one issue. While my winning statements are working, instantly declaring whether a player has one, my draw statement is not. When filling the last empty slot that would result in a draw, it instead acts as if it has made an ordinary move, and only on the subsequent move declares a draw. For clarification, the board is a list of lists. My code is as follows.

def move(self, row, col, user):
    """Places the users move on the board"""

    # Checks if the move is invalid and notifies the user
    if row not in range(3) and column not in range(3) and\
            self._board[row][col] == "x" and "o" or\
            self._current_state != "UNFINISHED":

        return False

    # Checks if any legal moves allowed and if so, places user on board
    elif self._board[row][col] != "x" and "o":
        if self._board[0][col] != user and self._board[1][col]\
            != player and self._board[2][col] != user or \
            self._board[row][0] != user and self._board[row][1] != user\
            and self._board[row][2] != user or self._board[0][0] != user\
            and self._board[1][1] != user and self._board[2][2] != user\
            or self._board[0][2] != user and self._board[2][0] != user\
                and self._board[1][1] != user:
            self._current_state = "UNFINISHED"
            self._board[row][col] = user

        # Checks for vertical wins and updates _current_state
        elif self._board[0][col] == user and self._board[1][col] == user\
                and self._board[2][col] == user:
            self._current_state = user.upper() + "_WON"
            return True

        # Checks for horizontal wins and updates _current_state
        elif self._board[row][0] == player and self._board[row][1] == user \
                and self._board[row][2] == user:
            self._current_state = user.upper() + "_WON"
            return True

        # Checks for diagonal wins and updates _current_state
        elif self._board[0][0] == user and self._board[1][1] == user\
            and self._board[2][2] == user or self._board[0][2] == user\
                and self._board[2][0] == user and self._board[1][1] == user:
            self._current_state = user.upper() + "_WON"
            return True
    # Checks if the board is full with no wins and declares game a draw
        else:
            self._current_state = "DRAW"
            return True
return True