How to use Classic Canon 6D to shoot video?

I recently bought a 6D because it's a cheap full frame which is very good for lowlight photoshoot and stuffs. Then I found out that the focusing on the 6D isn't that great. But it's still usable for photoshoot. But when I shoot video, it doesn't automatically focus unless I press the focus button.... show more I recently bought a 6D because it's a cheap full frame which is very good for lowlight photoshoot and stuffs.

Then I found out that the focusing on the 6D isn't that great. But it's still usable for photoshoot. But when I shoot video, it doesn't automatically focus unless I press the focus button. And what annoys me the most is that it changes the exposure when I refocus.

Please let me know if there's a way to use the autofocus when shooting video because using manual focus means that I cannot put it on my stabilizer.

If that's the way it is, then it's a real bummer for me.
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