Example 2 As shown in Figure 4, in a $7 \times 8$ rectangular chessboard, a chess piece is placed at the center of each small square. If two chess pieces are in small squares that share an edge or a vertex, then these two chess pieces are said to be "connected". Now, some of the 56 chess pieces are removed so that no 5 remaining chess pieces are in a straight line (horizontally, vertically, or diagonally). What is the minimum number of chess pieces that need to be removed to meet this requirement? Explain your reasoning $^{\mid 2\rfloor}$.

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Analysis: The difficulty ratio of this problem has significantly increased from 1, mainly due to its "apparent" asymmetry (the number of rows and columns are inconsistent). Therefore, the key to solving the problem is to find the symmetry hidden behind this asymmetry.
Inspired by Example 1, we will also start from the local perspective.
Solution: In each $1 \times 5$ rectangle, at least one chess piece must be taken. Following Example 1, as shown in Figure 5, the area outside the shaded part must have at least 10 chess pieces taken.

If at least one chess piece is taken from the shaded part in Figure 5, then the total number of chess pieces taken is no less than 11.

If no chess pieces are taken from the shaded part in Figure 5, then at least 2 chess pieces must be taken from each of the middle two columns, and at least 2 chess pieces must be taken from each of the middle three rows. Therefore, at least 10 chess pieces have been taken.

Considering the four squares (1), (2), (3), and (4) in Figure 6.

Looking diagonally, since the shaded area in Figure 6 indicates that no chess pieces have been taken, to avoid a line of five, the four squares (1), (2), (3), and (4) must all have chess pieces taken. Therefore, in Figure 6, 2 chess pieces are taken from the 3rd column and 2 chess pieces are taken from the 6th column; at least 1 chess piece is taken from the white area of each of the 1st, 2nd, 7th, and 8th columns, totaling 4 chess pieces; at least 1 chess piece is taken from the white area of each of the 1st, 2nd, 6th, and 7th rows, totaling 4 chess pieces. Therefore, 12 chess pieces are taken.
In summary, at least 11 chess pieces must be taken.
Figure 7 provides one possible method.