Proving Nonabelian Simple Group Can't Operate on Fewer than 5 Elements

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How can I prove the following:

A nonabelian simple group can not operate nontrivially on a set containing fewer than five elements.

I can't get started.
 
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When a group acts on a set of n elements, you get a homomorphism from that group into Sn. What can the kernel of this homomorphism be?
 

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