External FM antenna for my indoor stereo system

Hi Everyone,

I have a new Pioneer micro-stereo system at home. It comes with a single wire FM antenna connected to its rear socket with what I think is a Mini Micro JST 2.0 Ph 2-Pin connector with only one of the pins connected to this single wire.

Reception is awful and it's practically useless for listening to the radio.

I've been reading around looking for a solution.

First simple option is to find a better indoor antenna - any recommendation on something quick and simple, preferably "low-profile" that can improve something and won't be just a waste of money ?

Second option is to use an outdoor antenna. I've seen a lot of people recommending these omni-directional type which I think I can somehow install on my roof.

If I pick the second one I have two things to consider - how to deliver the signal from the antenna and how to connect it to the stereo system.

As for the first I see everyone is recommending an RG6 coax cable. Theoretically I can lay one but it would entail great efforts. Any way I can "ride" on the one already delivering SAT TV ? Can they live together somehow on the same cable ?

And then, assuming I was able to deliver the signal this way or the other from the antenna to the system, how can I connect the coax cable to the connector in my system ? Is it possible at all ?

Thanks in advance !