What verb should I use if I want to show another example?
Suppose I‘m giving a speech and have already given an example and I want to show the audience one more example, what verb is correct to be used in the following sentence?
Let's __ another example.

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My first response would be "try." It's pretty simple and the other examples are all fine too, but "let's try another example" is really pretty common and says what you want without undue wordiness.

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You can say, "Let's look at another example", "Let's take another example" or even "Let's consider another example." (you'd probably follow this last one with a hypothetical scenario).

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Let's _____ another example.

The following verbs/verb phrases can be used (in order for decreasing formality):
consider
look at
take a look at
see