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To divert the train to another track, a worker should have throw a lever in the control room.
 
 

This answer is incorrect.
"should have" is part of a past modal phrase. It should be followed by a past participle. It indicates a past situation. This is a statement of general fact and should be in the present tense.
 

The correct answer is
To divert the train to another track, a worker must throw a lever in the control room.

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