How to help someone who's venting to me, without feeling that I'm not being genuine?

Hi guys, hope you are having a great time!

This type of situation happens frequently to me, especially with women. And I usually try to make them feel they are being listened and that whatever situation that happened to them is unfortunate and that I'm for them.

The things is, whenever someone come to me to vent, I simply try to visualize the situation, from their perspective and in a neutral perspective and begin thinking about solutions and possible things that they didn't think about. But of course I know they don't want it, they just want a a friend to listen to them, and I get it, it's just not like how I process this types of situations.

So, I really do like to make them feel cared, but the words and attitudes that they probably want, aren't coming from me naturally, and that makes it feel forced.

Writing it made me realize that this is basically a vent aswell lol. But anyways, I would appreciate your answers.