re: Google Home Mini is currently $29.99..

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Can Echo control lights

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yes assuming you have some type of smart light installed. even the weirdo chinese wifi lightbulbs work with alexa

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thermostat

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yup, all of them that support wifi

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t.v.

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depends on what you want controlled but yes/kinda

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other things around the house?

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its synced with my corporate outlook account so when i ask alexa what does my day look like it runs through all my meetings and tells me the weather, etc. so 'other things' is a broad category. i can have my dot find my phone, intercom any other dot in the house and all kinds of local/gps related stuff