You'll need to find a listener that can detect the change of assignee and trigger a workflow transition.
I suspect the automation add-on can do this, and the Scripting add-ons you'll find in the marketplace can do it as well.
you can't do it without add-ons
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That isn't an out of the box feature. You'd need a plugin (I don't know if one exists for this) or write a listener.
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You need to use an add-on to install a listener that can execute your business logic.
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