Possible asbestos tile.. What to do?

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Hey everyone,

I've been working on tearing up an existing flooring so I can lay some new tile down. On top of the floor is hardwood, and about 3 layers of vinyl. The lowest layer of vinyl (red in picture) have me concerned about asbestos.

What would be the cheapest and safest solution forward? I assume that I will have to remove the hardwood flooring so that my tile will transition into the other area of the house. 

Also pictured, there are a few areas at the far wall where a few boards are missing. 

Opinions appreciated.

Thanks,

Andrew