19. (Wuhu City)

In a square plate $ABCD$ with a side length of 8 units, there is an equilateral triangular colored plate $OEF$ (vertex $O$ is painted red, $E, F$ are white) placed as shown (E coincides with D, and $EF$ coincides with $AD$). Now, the triangular colored plate rotates to the left with $F$ as the pivot until $O$ touches the $AB$ side, completing one "left move". Then, with $O$ touching the $AB$ side as the pivot, the triangular colored plate rotates to the left again, making the second "left move". This continues until the 1990th "left move" is completed and the plate stops. How far is the red vertex $O$ from point $A$ at this time? Explain your reasoning.
The "left advance" rule for the triangular color board is:
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(1) Every 3 left advances, the red vertex is inside the disk;
(2) Every 16 left advances, the triangular board returns to its original starting position, but the red vertex moves to the point F on the AD side;
(3) Every 48 left advances, the triangular board and its red vertex completely return to their original positions.
Since $1990=48 \times 41+22$,
1990 left advances are equivalent to 22 left advances. After 16 left advances, O moves to the F position. After another 6 left advances, the vertex moves to the midpoint P on the AB side, at which point $PA=3$.