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The statement that brake shoes should not be worn dangerously thin is true because the effectiveness of the braking system is heavily reliant on the condition of the brake shoes. Brake shoes play a crucial role in the braking process by creating friction against the brake drum to slow down or stop the vehicle. If the brake shoes are worn too thin, they may fail to provide sufficient friction, leading to longer stopping distances or even complete brake failure, which poses a significant safety risk.

Regular maintenance, including inspection of brake shoes, is essential to ensure they are within safe operational limits and to prevent excessive wear. If they become dangerously thin, drivers may experience braking issues, which can lead to accidents. Therefore, keeping brake shoes in good condition is vital for safe vehicle operation.